Eren: Beating the living shit out of someone cause they looked at him wrong
Armin: Figured out the governments secret plan to demolish humanity, and of course you can't have people as smart as Armin running around loose
Mikasa: Also beat the living shit out of someone because they slapped Eren (Though he was being a dumbass)
Jean: Stalking Mikasa
Marco: Framed for copyright infringement
Reiner: Murder, though he honestly didn't know he himself did it
Bertholdt: Crimes against humanity
Annie: Went on a killing spree, murdered dozens of people (whoops)
Sasha: Illegal possession of over 10,000 potatoes in her basement
Connie: Sneaking food to Sasha every night by breaking in her cell, eventually caught
Ymir: Punching a homophobe, and of course arrested by a homophobic police officer
Historia: Making a feeble attempt to hit the officer arresting Ymir, arrested with assault against an officer (Though it's bullshit)
Hanji: Multiple charges for making weird and illegal mixtures in their basement lab using military-grade chemicals
Mike: Harassment, smelling people constantly (a Karen reported him)
Erwin: Refusing to admit to false accusations. Was beaten then arrested.
Levi: Telling a police officer to 'Suck his Windex flavored ass-cheeks' Then punching them.