When the security guard puts the VHS tapes into the VCR to play Marge the tape of Bart stealing: the wall behind the TV is blank and the same color as the floor (with no line delineating the floor from the wall), yet in a wider shot, the wall behind them is full of TV's on green shelving; the security guard has moved further to the right; and the people behind them change. And when the tape goes in, Marge is holding Maggie, and Maggie switches to Homer without Marge handing her over.
While Bart is outside the Van Houten house it is shown to be a bungalow, but later after Milhouse tricks his mom into throwing him out, Bart is being shooed downstairs by Luann Van Houten. A bungalow does not need stairs.
When Bart makes a snowman version of himself a bird sits on top and the figure crumbles, but in the last scene the snowman is back intact.
The security guard tells Homer Bart broke the 11th Commandment, which is Thou Shall Not Steal. But that was the 8th Commandment revealed in the season 2 episode "Homer vs. Lisa and the 8th Commandment", also in the Bible, God gave Moses only 10 commandments.
How did Bart get caught shop lifting when Nelson And Jimbo Jones both got away with it? The part of the store where the camera caught Bart is right where they both showed Bart stuff they were stealing.