Factual error: Ryan, the laboratory technician, eats his lunch of burger and fries while discussing a murder case with Assistant D.A. Claire Kincaid. Trouble is, they are in his laboratory. No lab technician ever, ever eats or drinks in a laboratory - it is the most basic lab protocol imaginable. He could contaminate his samples in any one of a hundred ways, he inevitably contaminates his gloves or fingers with residue from his meal and he risks poisoning himself with accidental transfer. This is not a character error - lab security is hammered into science students starting with the first day of first year and number one on the list is never, ever eat or drink in your lab.
Other mistake: When the show aired in 1990, in the pilot episode Brenda falls for Jason. She later on reveals herself to be a "16 year old junior" in high school. Season 2 opens up with the gang on summer break which technically would make them going into their senior year. It wasn't until Season 3 that they were going into their senior year. They graduated in 1993 from West Beverly but the show debuted in 1990 so technically they should have been sophomores.
The Fresh Prince Project - S1-E1
Revealing mistake: When Will staples his Malcom X poster to the wall, the wall bends back and forth for a second or two.
Episode Nine - S2-E2
Continuity mistake: The necklace James took from the coconut in Dr. Jacobi's office in the previous episode had a gold chain. When he gives it to Agent Cooper in this episode, it's on leather.
So Long, Frank Lloyd Wrong - S7-E7
Continuity mistake: When Joe and Helen are talking to Y.M. Berg, there is someone at the AeroMass counter that is seen leaving twice.
Character mistake: Bobby gets injured in a racing accident. When the family is told by Greg that Bobby is paralyzed and can't walk, Marcia starts to smile, then quickly changes to a sad face to match the situation.
Dreams, Schemes and Putting Greens - S1-E4
Audio problem: When Maurice exhales at the end of his sentence as he protests the Japanese businessmen walking out of his house, the sound of his exhale is spliced off mid-way through. (00:38:55)