In the episode where Hillary obtains a job as a caterer there is a scene where Hillary is talking to the assembled group of her family. In this scene Will's apron disappears and reappears during shots.
When Carlton spends the weekend in Compton, Will tells Vivian and she becomes very upset. In one shot she takes an earring out of her ear but a few shots later Phil tells her to put her earring back in and the missing earring has switched sides.
During the weekend that Carlton is staying in Compton, there are posters on the wall of Jazz's apartment. Whenever the camera cuts in their direction, they switch walls, go in different orders, and are in different directions.
In the beginning of the episode where Aunt Viv and Uncle Phil go to Palm Springs for the weekend and Will can't go, he is wearing an inner tube that is under the left arm. In the next shot it is under the right and keeps moving back and forth.
In the first season, Hilary is discussing interviews with Geoffrey. Geoffrey asks her what her name is, and she replies "Hilary S. Banks". But, in the second season, when Baby Nicky is about to be born, Will's mother grabs Hilary and refers to her middle name as being Violet.
In the first episode ( "The Fresh Prince Project") Will is using a staple gun to put up a poster of Malcolm X. He repeatedly jumps towards the wall and punches the staple gun to secure the poster. Numerous times, when he hits the wall, you can see the wall shaking.