Game Breaker: One that was acknowledged and fixed: Deadpool's teleport in the first game. Essentially, it works by going for a spot a certain distance from Deadpool in the direction he's facing: if there's an area the player is allowed to go at that point, then Deadpool will instantly move to it. If not, he'll go as far as he can along that path. Elevation doesn't matter. Nothing in the way matters. Because of this, if used smartly enough this can be used to - in addition to getting places the player usually can't - skip whole areas of the level as the player is fully allowed to go through walls, Insurmountable Waist High Walls, voids and rivers, even burning wreckage as long as there is something to walk on on the other side. In the sequel, Deadpool's teleport was unsurprisingly changed so that it does not go through things the player is not allowed to go through, and the range is decreased to boot.
Ronin's "Spine Teaser" power is absurdly over-powered when used on larger enemies. Just how over-powered is it? When fully leveled up, it can kill Dr. Doom with one hit.
The sequel gives this status to Storm near the end, where the nanites allow enemies to share powers with each other. Their powers tend to be either telekinesis, fire or ice, the latter two being powers Storm is immune to, making a good lot of the challenge in the later missions including the final boss fight with Nanite-Fury.
Doctor Strange happens to have a spell that has a chance of... instantly killing any non-boss enemy in the game by turning them into a box. A box that can contain GOODIES.
Thor is this in MUA 2. Of the 3 Purposely Overpowered characters: Hulk, Thor and Jean Grey, Thor is the most overpowered. Hulk is a tank but is purely physical and Jean is purely elemental and a Glass Cannon: both of them can run into enemies and bosses that resist their damage. Thor however, has as much physical damage and defense as Hulk AND can dish out as much elemental damage as Jean thanks to his lightning. He's pretty much a walking brick wall and no enemy in the game resists both his damage types. The only reason to not use him is a Self-Imposed Challenge not unlike the above-mentioned Storm from the old X-Men Legends games.
Hulk is even more overpowered in the first game due to the fact that unlike the sequel, he actually does have a health regen ability in addition to his powerful attacks. When put into his "Fury" boost (which increases his size and attack speed), he is virtually unstoppable.
Harsher in Hindsight: Deadpool's fight with the devs of the game has them threatening to make Deadpool DLC. This was soon before all of the DLC for the game would become impossible to unlock without console commands.
Black Panther and Storm being part of the "Double Date" bonus after their disastrous breakup in Avengers Vs X-Men.
Iceman/Deadpool/Spider-Man/Human Torch: Why are [Iron Man and Captain America] so obsessed with each other, anyway? It's reaching "creepy ex" territory.
This, from 1:
Spider-Man: Hi, again. Shall we continue to discuss how wonderful Tony Stark is?
Narm: Penance in MUA 2. Also a fair chunk of Mephisto's dialogue, with the use of "astral energy" instead of "soul" and Nightcrawler's Small Nein.
In the first Pro-Reg mission, as soon as you run into the White Star, one of them says in the whiniest voice imaginable: "It's a raid! Get to your positions!"
You know those big hulking... things you run into at the omega base? Seem kind of intimidating, don't they? Then you run into them again in Asgard, and they talk. And they sound exactly like you'd expect them to. Another enemy that suddenly talks in Asgard is the Clay Warrior. His "Halt! You Shall Not Pass!" might have been Bad Ass if you hadn't just spent a level one-shotting about two-hundred or so of his kind.
In the first game, one of Doctor Doom's victory phrases after defeating an enemy is "Finally! I have achieved my ultimate triumph!". When he says this after defeating Random Mook #284, it's either this or Mundane Made Awesome.
Mephisto's Realm, oh dear god Mephisto's Realm. Not only is the level basically an Expy of Hell, but throughout the entire level you're pitted up against all kinds of demons that do things like swapping bodies with your character or trying to eat your character. Additionally, the level has a beyond-horrifying soundtrack that contains the sounds of thousands of trapped souls either moaning or screaming in ever-lasting torment. Sweet dreams.
In the second game the Pro-Registration side is using Mind Control to control villains and force them to hunt heroes for them. During one of the missions you can find a audio clip of Reed Richards casually explaining the device to what's presumably a room full of young scientists, while the victims villains, who actually volunteered to join their side (albeit presumably for selfish reasons), fruitlessly scream in terror while they're forcibly injected with mind suppressing nanites and their minds are subjugated in the background. It's somewhat more terrifying than it sounds. Later, the playable villain characters talk hatefully about how it felt to lose their minds and individuality to the Fold and agree to join, no-strings attached, if only to make sure that that sort of thing can never happen to them again. It takes a lot to make Reed Richards the most terrifying character in a game that includes characters like Venom and the Green Goblin, who you instead feel sorry for, but there you go.
I dare you not to feel a little unpleasant hearing Venom's breathing slowing as he's sedated. And then again maybe 10 seconds later when an unidentified female villain is brought in to be injected, all the while screaming for the S.H.I.E.L.D. personnel: "No! Get away from me! No!"
Stop Helping Me!: Stop knocking the demons off the altar, stupid CPU players! They only die permanently if you kill them on the altar!
Stop killing the exploding bugs, dammit! We need them to rig the teleporter!
They Wasted a Perfectly Good Plot: At the end of the First Game it's revealed that Galactus has sworn vengeance upon The Heroes and vows to destroy their planet for what they did to him during the course of the game. Sounds prime for a Sequel Hook right? Nope, instead all we get in 2 is a brief mention (that you might not even notice) from Thor about how he drove Galactus off when he came. also, Black Widow's betrayal was not touched upon in the sequel.
Tier-Induced Scrappy - Elektra and Blade in the first game were both considered pathetic - Elektra having no good attacks before level 22, and Blade having massive energy management problems. Not surprisingly, in the sequel, Blade was relegated to the last-gen versions, and Elektra was removed entirely.
The sequel has it's fair share of this, too: Daredevil doesn't gain any good powers, Venom has awful defense and low-damaging powers, and Penance had equally bad defense and a Game-Breaking Bug that prevented his unique mechanic, that his powers would deal more damage the more he gets hurt...granted, it was patched, but still.