In the scene where Alexander Falko hands the check for ten million dollars to Ernie, after writing the check he puts the pen on the table and in the next shot the pen suddenly appears again on his hand.
The mouse is hanging to a wire trying hard not to get sucked into the vacuum. It was somehow able to disconnect the sewage pipe and connect it to the vacuum tube. There's no way it would have been able to move the pipe with its tiny paws.
When Ernie and Lars inherit a mansion they hear that the last owner of the place was locked in a trunk up in the attic. They both come back to the house and one of the police officers said that Caesar was found locked in a trunk. A human is many times bigger than a mouse, so there is no way that a mouse that clever (with an elaborate obstacle course) could have carried him.
In the shot when Ernie and Lars head to the factory and we see the striking workers outside the building, a cargo container and a palm tree that are off-set are clearly visible to the left of the screen.
When the vacuum cleaner is attached to the sewage line, the mouse watches from outside. He sits on top of the upper ("outer") window panel which has been pulled down to the bottom position of its track (for easier cleaning - consistent with the boys housecleaning). Based on interior and exterior shots in the scene, the lower ("inner") window panel appears to run the entire length of the window. In addition, the position of the curtains change from framing the window to pulled back.
The goof item below may give away important plot points.
In the scene where Ernie is loading the shotgun to kill
the mouse, he knocks over a lamp with the shotgun. But shortly after that, the lamp is standing upright, and in the next shot, the lamp is down again.