The SRD has a few big contradictions with the core books, plus many minor inconsistencies
It's missing all changes made in errata since 2016
The Systems Reference Document was last updated to version 5.1 on January 12, 2016. However, it has not been updated at all since then. The FAQ on the linked page states:
Will more content be added to the SRD?
The full 5th edition game and its expansions are available for use via
the DMs Guild. New material will be added to the SRD if it is
necessary to keep this document and its contents updated to the latest
The PHB received errata in 2017, all 3 core books (the PHB, DMG, and MM) received a larger round of errata in 2018, and the PHB was once again updated in errata in 2020. However, despite the second sentence of that answer, the SRD hasn't been updated to match the changes to the corresponding portions of the 3 core books.
Several examples of these discrepancies follow; if you're not interested in such details, skip to the latter potion of my answer.
For instance, the 2017 PHB errata says:
Glyph of Warding (p. 245). The first sentence clarifies that the magical effect needn’t be harmful. The final two sentences of the first paragraph now read as follows: “The glyph can cover an area no larger than 10 feet in diameter. If the surface or object is moved more than 10 feet from where you cast this spell, the glyph is broken, and the spell ends without being triggered” (6th printing).
However, the first paragraph of the description of glyph of warding on p. 149 of the SRD reads:
When you cast this spell, you inscribe a glyph that harms other creatures, either upon a surface [...] or within an object that can be closed [...] to conceal the glyph. If you choose a surface, the glyph can cover an area of the surface no larger than 10 feet in diameter. If you choose an object, that object must remain in its place; if the object is moved more than 10 feet from where you cast this spell, the glyph is broken, and the spell ends without being triggered.
As you can see, the description in the SRD doesn't match the current description of glyph of warding, which says:
When you cast this spell, you inscribe a glyph that later unleashes a magical effect. You inscribe it either on a surface [...] or within an object that can be closed [...] to conceal the glyph. The glyph can cover an area no larger than 10 feet in diameter. If the surface or object is moved more than 10 feet from where you cast this spell, the glyph is broken, and the spell ends without being triggered.
This difference does have mechanical implications; the original description of the spell doesn't limit the size of the object, and doesn't state that the glyph breaks if the object is moved.
Likewise, the 2018 PHB errata makes a number of modifications; most of them are minor wording clarifications, and some affect content that's not in the SRD, but one of them affects the advantage and disadvantage rules:
[New] Advantage and Disadvantage (p. 173). In the first sentence of the fourth paragraph, both instances of “reroll” have been changed to “reroll or replace.”
However, on p. 76 of the SRD, that sentence says:
When you have advantage or disadvantage and something in the game, such as the halfling’s Lucky trait, lets you reroll the d20, you can reroll only one of the dice.
This is an important change, because it affects how advantage and disadvantage interact with things that replace a roll, like the School of Divination wizard's Portent feature (though it's not in the SRD) or the glibness spell (which is on p. 149 of the SRD).
The full list of changes in the 2018 PHB errata is too long to list here, but suffice it to say that it changed plenty of spells (e.g. contagion) - and the exhaustion condition, and the rules for grappling and shoving - in significant ways, and none of those changes are accounted for in the SRD.
The 2020 PHB errata only changes 2 other things, and only one of those things appears in the SRD. The description of the Heavy property on p. 65 of the SRD says that "Creatures that are Small" have disadvantage on attack rolls with weapons with the heavy property; the errata changes this to apply to Tiny creatures as well. This may seem minor, as it's already a logical extension of the rule, but technically the property originally didn't affect Tiny creatures at all. The errata fixes that, and the SRD does not include that fix either.
Dungeon Master's Guide
Although examples from the DMG and MM aren't relevant to your exact use-case (since players ostensibly aren't looking at DM-facing materials most of the time), these discrepancies are still important to note. For instance, the 2018 DMG errata says:
[New] Rod of Lordly Might (p. 196). The following text is appended to the sentence on button 1: “(you choose the type of sword).”
However, the corresponding text on p. 240 of the SRD is missing this parenthetical:
If you press button 1, the rod becomes a flame tongue, as a fiery blade sprouts from the end opposite the rod's flanged head.
This isn't a contradiction so much as it is an omission (where the SRD is missing a clarification that was added to previously ambiguous text), but it's just another example of how the SRD can differ from the rules.
As for the 2018 MM errata, nearly every change affecting a monster that appears in the SRD causes the updated Monster Manual to "contradict" the SRD, since almost all of them change a saving throw modifier, skill modifier, attack roll bonus, or damage roll from one value to another. For instance, it says of the efreeti:
[New] Efreeti (p. 145). Innate Spellcasting: “3/day” changed to “3/day each.”
The corresponding portion of the efreeti's Innate Spellcasting trait on p. 310 of the SRD says:
3/day: enlarge/reduce, tongues
1/day each: conjure elemental (fire elemental only), gaseous form, invisibility, major image, plane shift, wall of fire
This is a notable difference, because the version in the SRD makes it seem as if efreeti can cast any combination of enlarge/reduce and tongues 3 times per day in total, when in fact the efreeti can cast each of those two spells 3 times a day.
Likewise, for the purple worm, the MM errata says:
[New] Purple Worm (p. 255). Bite and Tail Stinger: +14 to hit [each was +9].
However, the statblock on p. 341 of the SRD (continued from the previous page) still includes the incorrect "+9" attack roll modifier (instead of +14), which is a dramatic difference - especially considering bounded accuracy.
There were other errors in the SRD even before errata
Even ignoring errata, parts of the SRD were inconsistent with the published rules even when the SRD was created/updated - particularly in the descriptions of certain magic items. For instance, the description of the sword of sharpness on p. 246 of the SRD says:
When you attack a creature with this weapon and roll a 20 on the attack roll, that target takes an extra 4d6 slashing damage.
However, the description of the sword of sharpness on p. 206 of the DMG says the target takes an extra 14 slashing damage, not 4d6. This distinction is especially important because a natural 20 on the die roll is typically a critical hit, which causes all of the attack's damage dice to be rolled twice - including any extra damage dice added to the same attack. If the extra damage of the sword of sharpness were 4d6, this would actually be doubled to 8d6 (unless something caused it to become a regular hit instead of a critical hit).
However, as lead rules designer Jeremy Crawford unofficially clarified in a January 2018 tweet:
The sword of sharpness deals an extra 14 slashing damage when you roll a 20 on its attack roll. The SRD incorrectly says otherwise. Note that the SRD is not an official rules source for D&D.
The same discrepancy exists for several other magic items as well. The mace of smiting (DMG, p. 179) says that a nat. 20 on the attack roll does "an extra 7 bludgeoning damage, or 14 bludgeoning damage if it's a construct", but SRD p. 229 incorrectly lists these values as 2d6 and 4d6 respectively. Likewise, the sword of life stealing (DMG, p. 206) does an extra 10 necrotic damage on a nat. 20 and grants the wielder 10 temp HP, rather than 3d6 damage (and equivalent temp HP) as SRD p. 246 indicates. And finally, a vicious weapon (DMG, p. 209) deals an extra 7 damage on a nat. 20, not 2d6 as SRD p. 248 says; this discrepancy resulted in its own Q&A here (and another Q&A about the interaction of the supposed 2d6 damage roll with the critical hits rule).
The SRD isn't an official rules source
As Crawford's tweet mentions, the SRD is not an official rules source. As the description of the SRD on Wizards of the Coast's official D&D website says:
The Systems Reference Document (SRD) contains guidelines for publishing content under the Open-Gaming License (OGL).
I elaborate on what this means in an answer to another Q&A about the interaction between SRD versions of material and published versions of the same material, where I reiterate that the SRD is not an official rules resource (and thus material from it is not a consideration in the official rules):
Essentially, the SRD details what official D&D 5e material can and can't be (re)published by others using the OGL. (It doesn't preclude other methods of legally publishing D&D material, such as under the terms of Dungeon Masters Guild (DMsGuild).) Notably, it's not intended to function as even a partial list of the 5e rules; the material contained within the SRD is just a comprehensive list of what's allowed to be published under the OGL.
Because the SRD is not official rules material, whenever the SRD conflicts with the latest version of the published rulebooks, the latest published rulebooks always take precedence. The SRD merely attempts to reflect some of the core rules in determining what D&D 5e material can be republished by others, and even the material included within it does not always match the versions in the source books (as detailed throughout this answer).
(Note that D&D Beyond does list all material that appears in either the SRD or the Basic Rules PDF as being from the "Basic Rules" - even though the Basic Rules and SRD have several important differences, both in purpose/function and in the content included. D&D Beyond's "Basic Rules" listing is an inclusive combination of the two separate documents from Wizards of the Coast. However, for material that appears both in the SRD and the Basic Rules PDF, the descriptions always match the most up-to-date and official version of the material - i.e. the published books.)
All in all, this answer is merely intended to point out that the SRD does, in fact, now contradict the official rules in a number of places, due to later errata as well as existing discrepancies. Many of the changes in errata are minor clarifications, but some do have significant mechanical implications. It's nevertheless important to keep these distinctions in mind when attempting to play the game using the SRD rather than the core rules, especially when some participants are relying on the SRD while others are using the published books.