Character mistake: When April goes to see Hank at his motel, he states her romantic feelings for him are a result of "Nightingale Syndrome," however, the Nightingale Effect is caused by the caregiver developing romantic feelings for the patient, not the other way around.
Continuity mistake: Jill writes Hank a goodbye letter which she hands to a friend to deliver. In the letter which Hank reads the next day, Jill states how beautiful Africa is and how Hank must visit. She wrote this before she left and had not seen Africa yet.
Continuity mistake: Divya places a pizza slice on the table in front of Hank with the pizza crust toward the right of the screen. In the next shot with Hank's arms still at his side, the plate with the pizza is now positioned further to the left of the screen and the slice is turned so that the crust is now on the left.
About Face - S4-E6
Continuity mistake: Hank boards Boris' helicopter, but just before he does the helicopter is shown in a wide shot with no one nearby. Hank boards and a guard closes the door from the exterior. Seconds later the helicopter takes off and a wide shot shows no one on the ground. The guard appears out of nowhere and then vanishes.
Continuity mistake: In the final scene, Hank, Boris, and Dmitry are walking toward the helicopter. In the background, white, red and black helicopters are visible. When the camera switches to a close up of Hank and Boris, all three helicopters are gone. The camera then switches to Christina and in the background, a single blue helicopter is now on the helipad.
Something Fishy This Way Comes - S4-E13
Continuity mistake: When Dmitry and Hank are talking while waiting for Amir to return, Boris approaches Dmitry and hands him a drink. The drink is initially in Dmitry's left hand, but when the shot cuts, the drink has jumped to his right hand. (00:26:35)
Continuity mistake: Early in the episode Divya is helping the repo man with the antique airplane on the grass just off the beach at a private home. The homeowner appears and the repo man starts to take off, and magically a long runway appears out of nowhere.