Druids and Clerics (and also Paladins and Rangers) have, compared to other spellcasters, the advantage that they can prepare spells from a fairly big pool of spells. Now, if you let your players choose spells from the Spell Compendium this increases the available spells for Clerics and Druids immediately and also for Wizards, if they can copy them. Sorcerers, Bards and Assassins however don't greatly benefit from the inclusion of these new spells in the game, while all non-spellcasting Classes don't benefit at all. Isn't this a serious imbalance?
It is imbalanced, but not because of Spell Compendium
The imbalances you note are very real. They have often been noted, commented upon, and even codified in the 3.5 tier list.
Clerics and druids, along with archivists and wizards,1 simply are the most powerful classes in the game because they have access to all of these spells and can change them every day.
Sorcerers are a tier below, because they have access but cannot change them.
Bards are a tier below that, because they only go to 6th-level spells.
Rangers are another step down: only 4th-level spells.
Fighters are a tier below that, because they have no spells.
This marginally over-simplifies the tiers, but it's pretty close to true: spells are, in 3.5, just about equivalent with power. Only a few classes meaningfully change tier despite their spells or lack of them.2
But this is not because of Spell Compendium. This isn't even because of supplements in general. This is due to some fundamental design mistakes that Wizards made early on. They underestimated spells, overestimated the significance of what non-magical types were doing. Player's Handbook is the most imbalanced book they published; they slowly learned from their mistakes and did better in future products (well, mostly).
So clerics and druids have this advantage; yes, absolutely. And it's a big one. But (very nearly) all the best spells are core anyway. Adding Spell Compendium (or any other source of spells) doesn't matter very much to them, since optimally 90% or more of their spells will be still be core.
The bard, paladin, and ranger are actually the big winners: instead of just getting mostly the same spells the bigger classes got many levels ago, they actually get some unique stuff, greatly expanding their ability.
Fighters are still left in the dust, but they were always there. Not much can be done about them; they weren't well-designed. Better to replace them, such as with Tome of Battle classes. But even failing that, Spell Compendium doesn't make them worse, it just means a few classes that would otherwise be down there with them get to start to move upward.
Spell Compendium is a good book, full of interesting material, that avoids a lot of the overpowering mistakes of the core spells. Clerics and druids may find a few things to pick up, but ultimately most of the spells are weaker. The book is really best for half-casters.
2 spells per level plus any others you come across is plenty, particularly off of those spell lists. There are numerous ways to build a wizard to improve on the 2 spells/level if one anticipates a game where spells will be few and far between, but ultimately you don’t even need to – forty spells from the Sor/Wiz list is just a phenomenal amount of potential power.
Some example exceptions from “more spells = higher tier” include
• The Eberron Campaign Setting artificer: Tier 1 along with archivist cleric, druid, and wizard, despite only 6th-level “spells,” thanks to incredible versatility provided by their item-creation abilities
• The Miniatures Handbook healer, which is Tier 4, with the ranger and below the bard, despite cleric-style spellcasting up to 9th level, since their spell list is incredibly one-dimensional and weak.
There are a few extremely powerful spells, many powerful spells, and very few situation-dependent spells that matter enough. Often you won't know you need those spells until it's too late to prepare them, in any case.
There are no spells in spell compendium that change any of that in any way. Additionally, there are few overpowered spells there, and so few that a sorcerer/favoured soul could comfortably just have them as spells known.
Even the worst spell compendium spells (published at the end of 3.5's run) are nowhere near as overpowered as the worst PHB spells (published at the start of 3.5's run). Shapechange and Time Stop and Glitterdust leave everything in the SpC in the dust.
What SpC does is give more 'themed' and 'oddball' spells. If your prepared casters pick spells from there, they'll definitely seem more eclectic and 'prepared' compared to the sorcerer/favoured soul/bard etc. But their power level will be exactly the same.
First of all, as usual "imbalance" is what you make of it. If players in your game are having fun even though one's a "lowly tier 4" fighter and one's a "CodZilla," no amount of CharOp theory matters. So if you're not having disparity that affects your fun now, you're not going to with the Spell Compendium either.
In my experience, a lot of the punch in the Spell Compendium is stuff that lets you get around saves/spell resistance more easily (orbs etc.) and otherwise gives more options to target any weak spot something might have. Ray of Stupidity drops any low-int creature to a coma in one shot. If you're playing a higher level game with a lot of high-save, SR-having opponents, this means the role your martials may have been playing could be reduced, if they were the ones shining when the mages couldn't directly affect demons and golems and whatnot.
Though the effect on your game depends on your wizards' tactics - I liked using Benign Transposition to swap a party martial in for myself when some critter thought it would be clever to go after the caster. And Brilliant Blade/Brilliant Aura to give all the martials brilliant weapons. (We ripped through a huge lair of giants in Rise of the Runelords with that... Though I got a lot of Ray of Stupidity kills there myself.)
If you have players who don't play as a team and just try to outdo each other, it could be an issue. "I spam Castigate! Sure, some of my party will take half damage but yay, I get to hurt moar enemies!!!" If you have players who try to empower others on their team, a lot of the SC spells actually give martials a chance to shine.
No (for non pure casters)
The spell compendium has a lot of spells, a lot of which are (very) situational spells. Versatility is however a spellcasters friend, the addition of spells that for example allow you to instantly know the geography around you (Lay of the Land) are not really unbalancing but add general out-of-combat usefulness to an otherwise poor caster class (Ranger).
There are however also spells that offer a significant bonus in combat to the weaker caster classes (let's take ranger again) like 'Embrace the Wild' which gives a ranger the chance to fight in darkness (via blindsense) or locate/track an enemy through smell (via scent).
The above types of spells, while nice, do not unbalance the game in my opinion since they mainly bring the non true caster classes closer to the true caster classes (Wizard, Druid and Cleric).
Possibly (for pure casters)
The book does however also contain spells that do imbalance the game. A prime example of those spells is the 'Bite of the Were...' line, which offer a melee (polymorph) druid a huge bonus to all her melee stats. Bite of the weretiger (Druid 5) for instance adds +12 enhancement bonus to Strength, a +4 enhancement bonus to Dexterity, a +6 enhancement bonus to Constitution, and a +5 enhancement bonus to natural armor. The spell also gives the benefits of the Blind-Fight and Power Attack feats. The result of that is that a druid, using these spells will make a simple fighter completely obsolete and thus unbalancing the game further than it is by default.
There are also spells such as blinding spittle (ranged touch attack for blindness, no save), which are horribly broken (in the right situation). These type of spells can basically end a combat instantly if the enemy has no access to water. I have seen this spell (blinding spittle) being used effectively in the abyss/baator, considering that demons/devils generally don't carry a liquid around.
Other type of spells from the SC that are a bit unbalancing are spells that are harder to resist than their player's handbook contemporaries, the orbs that mxyzplk already mentioned are a prime example of that.
There is another aspect that one should realize when thinking about if certain spells unbalance the game. Pure caster characters are by definition stronger (due to versatility) than martial characters. A simple fighter that knows that he has to fight in a dark can prepare by drum roll bringing a light source (assuming that he is not able to afford a blindfold of true darkness). A pure caster however has more options available to him (also with just the player's handbook) that I wish to list here.
It can, it depends heavily on how the people in the group play and have built their characters.
No! Having played a wizard, these did not allow me to obliterate enemies. A smart DM knows what spells you know & how to make fair encounters. Most spells here do not give you "MUAH HA HA - total power," just new options (like seeing in magical darkness. Obviously, spell casters are still limited by spells per day & what they know. Wizards would have to know what to bring. (Are we sneaking over to your DM's house & reading his plans for your next adventure to better prepare?)