Continuity mistake: Near the end of the episode when Nico is burning the photo of her father, she burns it at the top left corner in a close-up shot. Then in the following shot the photo is suddenly burning at the top right corner instead.
Character mistake: One of the characters, Agent L, is usually talking to the kids via some gadget with bad audio. In The Golden Gauntlet, the first time she appears on the screen she misnames Agent J, calling him "Agent G." She then later in her speech calls him by his name correctly.
The Gang Tries to Serve a Subpoena - S4-E2
Continuity mistake: Luca and party are about to board a green private jet. Moments later when they take off, the shot shows the forward underside of a white plane. At first I thought that maybe it was white on the underside, but the nose wheel well doors are indeed green, and the takeoff picture shows an airplane with white nose wheel doors. (00:19:40)