Plot hole: If Andy really did enlist into the Army Reserves and "forgot about it" like he claimed his name would have been flagged as a deserter when he was arrested for pot possession in the episode "Lude Awakening." With that, the police would have called the Army and he would have been returned to military control to face desertion charges.
Factual error: In Season 3, Episode 13 ("Risk"), Nancy takes her son Silas to an 'underground' doctor used by gang members following an attack by a biker gang. After she tries to negotiate a lower price due to the lack of anesthetics, the doctor says that he can get a second opinion at a hospital and order a $10,000 MRI if she would rather pay for that. However, an X-Ray is the first, less-expensive method used by emergency rooms and trauma centers to confirm a fracture. An MRI is typically only used to evaluate skull/brain-related injuries, but is a rarer utilized, expensive second option to evaluate a fracture that generates an unclear X-ray.
Continuity mistake: Doug has his son Josh kidnapped from his own home twice. The second time Josh answers the door wearing a dark long sleeve shirt, but when they cut out for a second and go back, Josh is bagged in the hallway wearing a short sleeved, lighter shirt. It's the same shirt he wore the first time.
Visible crew/equipment: When Nancy gives the story about being aware of her people there's a flashback to when she's at the space exhibit with Stevie. If you look to the right of the screen when she's hugging him, you can see the shadow of the boom operator's microphone being held above their heads on the back curtain behind Stevie and Nancy.
Continuity mistake: When U-turn is going to investigate Sanjay's sneeze, he is pointing the gun over his wrist. In one shot, his right wrist is resting on his left wrist, in the next the barrel of the gun is resting on his wrist and it changes back and forth.
Continuity mistake: When Nancy starts her maid job at the hotel she enters a room with a wig looking around at all the mess. When the shot changes to her going to the restroom lifting the toilet lid she has no wig on, then when the shot switches back she has her wig back on.