While it is hard to know every spell ever printed and cross-compare all of them to find potential imbalances, it's important to note that most overpowered 4th-level spells are available in the core rules. Expansion books generally toned back some of the more egregious power spikes that casters could leverage, so this answer will mostly focus on stand-out core spells and how they could be addressed. Some spells from other sources will, of course, be considered.
Balancing Options
There are a few ways to incorporate higher level spells in e6 that I will be referring to in shorthand. In a general sense, they are:
Attach to items
4th level wands and scrolls can be put into an e6 campaign pretty easily, as any particular imbalance will sooner or later sort itself out when the item is expended. This is the safest way to go, and it could even be used to "test run" a spell before deeming that the party should be allowed to have it.
Limit practicality
This is any restriction that makes a spell harder to use on-demand, most obviously by increasing casting time. A one-minute casting time would shut down most combat spells, and a one-hour casting time would limit all but the most ridiculous out-of-combat spells. You could also make adjustments such as obscure ritualistic prerequisites - maybe you have to cast the spell while underwater, or maybe you need to draw magic circles on the ground. Something that prevents flexible usage of the spell on-demand.
Add drawbacks
Make the spell eat more spell slots, give it a hefty material component, make it inflict self-damage or ability drain, or some similar effect. This is a pretty light counterweight given the power of 4th level spells, but it could work for most any spell not specifically mentioned below.
Problematic Combat Spells
These spells, if not specifically addressed, give spellcasters a distinct advantage in fights and begin to change the dynamics of how spellcasters interact with combat.
Dimension Door, Psionic Dimension Door
As mentioned in the question, it's an easy get-out-of-jail-free card. It shuts down entire melee builds single-handedly by making grappling significantly less effective. Attaching this to an item would generally be fine because of how hard it is to draw items in a grapple, and limiting the practicality of the spell would eliminate most issues as well. If you want to put a drawback on this spell, something that limits the caster's actions after teleporting would be very effective. If, for example, the spell applied the Dazed condition for a few rounds, it would allow the grappling character to remove the caster as a battlefield threat while still letting the caster escape immediate harm. All of this without creating significant issues for the spell's less problematic out-of-combat uses.
Solid Fog, Radiant Fog (Book of Exalted Deeds)
Even more of a melee-denier than Dimension Door, with the added bonus of protecting the caster's entire team instead of just the caster. In my experience, this spell is very reliant on how skilled the player using it is. A bad use of Solid Fog can do more harm than good, but clever use of it can shut down an incredible number of fights. If you don't know where your players are going to land, make absolutely sure you don't put this on a wand. This is also a hard spell to balance with drawbacks, since it generally gets used in the first round of a fight when the caster is best able to eat a downside. Defintely best to balance this one with an increased casting time.
Greater Invisibility
Turns any rogue into a nigh-unstoppable murder machine against a significant number of opponents, and it's a potent buff on everyone else too. Certainly hampered by an increased casting time thanks to a short duration, though. Pretty easy to pull back in line, mostly because the very nature of being a buff spell makes it feel much less oppressive at the table than it otherwise would be. It's strong, obviously, but it doesn't hog the spotlight in the way that Solid Fog does, so it's far less problematic.
Lesser Globe of Invulnerability
This spell outright denies 1st, 2nd, and 3rd level spells, which is the vast majority of spells in an e6 setting. The short duration makes it similar to Greater Invisibility in a lot of ways, where this spell is significantly more potent at the cost of being more situational. An increased casting time should bring it in line, though it still may invalidate a few fights if the party gets the drop on some mages.
New Player Capabilities
These spells grant completely new capabilities to the party that may alter the kinds of challenges you can throw at them. They're particularly difficult to nerf into a less disruptive state, too, so either prepare for them or just ban them outright.
Locate Creature, Scrying, Arcane Eye
4th level is when divination gets good. Players with access to 4th level spells will become significantly more capable of scouting out enemy bases and will be generally more well informed about the situations they're getting into. This effect may even offset the effects of nerfing other 4th level spells by increasing casting time; if the party knows what's on the other side of a door, they can take as long as they like to cast a perfectly placed Solid Fog. For this reason, putting some kind of drawback on these spells would really be the only way to keep them from becoming overcentralized.
Remove Curse
A lot of e6 campaigns use curses as major plot points because of how sticky they are without Remove Curse being around. If your campaign's plot revolves around curses and mind control, this spell is probably best kept out of player hands.
Contagion
Most heroes wouldn't dare use this spell. Particularly cruel parties, however, can use this spell to break entire cities thanks to how much harder it is to deal with diseases in your typical e6 world. Maybe that's the vibe you want, but it's nonetheless a really powerful bit of leverage available for evil casters that no amount of drawbacks can meaningfully stop.
Sending
Clerics get Sending as a 4th level spell, and the very existance of this spell changes how global communication works. Perhaps fitting as a capstone ability for a spellcaster - just be aware of the possibility of this spell cropping up when planning your adventure hooks and either ban it outright or put a material component on it if you're not ready for that. A magical payphone is a lot more managable than a magical cellphone.
Spells to Be Aware Of
You may not need to do anything specifically about these spells, but they can catch an unprepared DM off guard.
Phantasmal Killer, Call of Stone (PHB2)
Save-or-die spells aren't significantly above the typical power level expected for e6, but they can wreck some encounters in unexpected ways.
Death Ward
On the other side of the coin, any big bad archvillain using Finger of Death or Phantasmal Killer may find it a bit more difficult to pull off than you would expect if the party has a cleric packing 4th level spells.
Corporeal Instability (Planar Handbook)
A very potent save-or-suck spell that isn't limited by creature types. There are a few other similarly debilitating spells out there, too, so just be ready for spells to turn entire encounters on a single failed saving throw.
Detect Scrying
Be aware of this if your big bad likes scrying - it makes it a lot easier for the party to have secret conversations.
Wall of Salt (Sandstorm)
While not unbalanced for any combat or utility purposes, this spell can be used to make a lot of money very easily. Summon the wall, sell the 18 cubic feet of salt from the wall for ~6,750 gold, repeat as needed. I would reccommend ruling that the salt from the wall is far too impure to sell, or that it magically degrades and becomes useless a few minutes after being ground up.
Psychic Reformation
This 4th level psionic power is generally used to cheese prestige class entry requirements and thus wouldn't be as flexible in e6, but shuffling feats around is still pretty valuable when all of your post-6 progression comes from them. This may become particularly potent if your 4th level spells/powers are coming from feats, though thankfully most psionic powers are very well balanced.
Last Note: Metamagic
There are a few metamagic combinations that start to open up if 4th level spells are on the table. Most, like your typical Empower Spell and Maximize Spell, aren't too bad. However, Quicken Spell suddenly becomes an option if combined with metamagic cost reducers like the Arcane Thesis feat or the Practical Metamagic feat. Quicken Spell has a well-earned reputation for being a combat-breaking machine, so it may be safest to just exclude spells with metamagic from whatever your source of 4th level spells is.
