Homer strangles Bart for a couple of times.
Bart plays a video game where babies are zapped with a lazer.
Mild comic violence.
In a cartoon within the movie, a character is stabbed repeatedly by a flagpole (no blood shown) and is blown apart by an explosion (no blood shown).
Martin stands up to a bunch of bullies, beating them up with a big pole, knocking them down.
A mob, featuring the other characters who have been on the show ( such as Apu, Jimbo, Snake, Dr. Hibbert, and Krusty the Clown ), attempt to blame Homer, by trying to kill him, and later his family. They all have very threatening angry looks on their faces, rakes, torches, guns, and ropes. The mob is later foiled after the Simpsons jump into a sinkhole that sends them out of the dome, to be away from being murdered.
A robot shoots itself in the head.
Homer gets a hammer caught in his eye.
Homer gets hit by a wrecking ball and is hit between a giant rock and "a hard place"
A penguin in a video game is shot by a walrus.
Before Russ Cargill is about to shoot Homer and Bart, Maggie pushes a rock/boulder on his head, assuming that he is killed.
Mostly the violence is slapstick and intended to be funny.
A man is killed by a giant shard of glass, hitting him in the crotch.
A man is crushed by the corner of a glass dome. No blood or violence is shown, he is just comically flattened.
A large, glass dome explodes and shards of glass (big and small) rain down on the citizens of Springfield.