Character mistake: At the ravine, upon learning that the bridge doesn't exist yet, Marty states to Doc "We can't wait a year and a half for this to be built". If you carefully look at the sign, it says the bridge is opening Summer 1886. That's under a year away, not a year and a half from Sept. 1885.
Character mistake: When Raphael is chasing Casey Jones after their fight he vaults over a taxi hood, never takes his eyes off Casey, but he somehow loses him.
Suggested correction: 2 things are happening; a shell backed stocky Raphael is chasing a lighter human athlete Casey. Casey has freedom of movement, whereas Raphael can't stray much from the shadows in hiding. :-) A knocked out Casey wouldn't be helping the Turtles out of the next evening with that memorable entry so I'm glad Raph lost the chase.
Character mistake: When Harrigan is watching the surveillance video by Bill Paxton he states that the helicopter is a silver Alouette when it is actually an AS-350.
Character mistake: Given Billy still remembered and recognized him it seems strange Kate doesn't when she mistakes Daffy for Gizmo.
Suggested correction: Billy spent significantly more time bonding with Gizmo in the first movie - days and days. By contrast Kate had very little actual time with him.