Continuity mistake: When Jack is on the phone explaining why he can't go into work again because he's really hiding at home from the bully Max, there is a chair wedged up against the front door. Larry knocks and when Jack is sure it is indeed Larry, he unlocks and opens the door without the chair in the way any more.
The Not-So-Great Imposter - S5-E9
Revealing mistake: In Angelino's kitchen, when Mr. Angelino comes in and mentions steaks for eight people are needed, look behind him at the door's window. Janet is briefly seen watching (as if waiting for her cue to enter), then quickly ducks out of sight. A second later, she's seen again while Angelino asks Felipe to help him in the freezer. She then runs in the door with Furley as if they first arrived at that moment.
Continuity mistake: When Furley enters The Apartment at the start of the party, the outside weather is crystal clear. Less than 2 minutes later, Furley tells "Austin" the fog is very heavy and the airport is closed down. Then upon opening the front door, tons of thick fog is all over outside. While fog can roll in very quickly, how could Furley even bring up the fog in the first place when it was not there at all when he walked in?
Visible crew/equipment: When Janet's father hands Jack the big gift, a microphone appears for a second at the top of the screen. (00:03:15)
Visible crew/equipment: In the scene where Maxine comes out of the bathroom and yells "Jack" a microphone appears for a second at the top of the screen. (00:25:05)
Character mistake: When Jack tells Mr. Furley his brother is in town (before mentioning it was a "twin" brother who Jack made up), Mr. Furley gave a puzzled look and said "Your brother?" which appeared as if he didn't know Jack had a brother. However, in the previous season, Mr. Furley briefly met Jack's brother Lee, so he already should have known Jack had a brother (even if were to turn out to be a different brother).
The Not-So-Great Imposter - S5-E9
Revealing mistake: The kitchen of the husband with the cheating wife is the same kitchen used for Chrissy's parents house in Fresno at the very end of the next episode end of episode "Jack's Other Mother" (S05E10).
Upstairs Downstairs Downstairs - S5-E1
Visible crew/equipment: Shadows from the booms are quite visible in varied takes, along with false ceiling in the living area of their apartment.
The Case of the Missing Blonde - S5-E21
Plot hole: After being stuck inside the phone booth, the police officer arrests Larry for vandalism after Larry breaks the glass in the phone booth. In a real-world situation, an officer would most likely let someone go without arrest if the person got stuck inside like that (declaring an emergency) and couldn't get out without breaking the glass.
Visible crew/equipment: Obvious shadows from booms, overhead, and crew members reflect off the walls while Jack and Larry are talking, and Larry looks like he's either reading from cue cards or following an off-camera director for his blocking moves.
The Not-So-Great Imposter - S5-E9
Plot hole: All these characters (the bookie, policemen, the sister, the husband) were after David Miller and all come to attack Jack in some way (thinking Jack is David Miller). However, a big city like LA most likely has several David Millers so why would they all assume this David Miller is the one they're looking for? So even though Jack's name could have been David Miller, how would everyone think he is the one they're looking for?
Suggested correction: These are questions, not plot holes. First, Jack and the restaurant are in Santa Monica, not LA. At the time, Santa Monica had a population of around 88,000. While the article was printed in the LA Times, there wouldn't be a lot of famous, professional chefs, working/living in Santa Monica named David Miller.