Continuity mistake: The hole Max makes in the wooden gate changes in shape when the thugs reach it. Max crashes through, leaving a hand shaped hole, but as the thugs reach it, the 'thumb' has disappeared.
Revealing mistake: After Max the dog breaks free from the cage and then bites through Callahan's chains, the two head to the metal barred window and Max begins pulling on one of the bars with his teeth. Which are obviously rubber, as they 'bend' slightly as the dog is pulling.