Thanks for the Memories - S4-E1
Factual error: Sean Renard is seen going into 'asystole' at The End of the episode (flat lining) and the doctors use a defibrillator to shock his heart, but a defibrillator is useless with asystole. It is only used to correct abnormal heart rhythms (fibrillation). Defib-ing an asystolic heart is like trying to reboot a computer device with no power supply.
Character mistake: When Nick and Hank talk about going through the park, Hank says "come on, David." David is Nick's real name.
Continuity mistake: When the woman falls near the beginning, her arms are out to her side, almost making a T shape, even after she stops moving. In the next shot, her arms are down by her side.
Tarantella - S1-E11
Character mistake: Hank's action as a cop towards the man on the boat makes no sense when going after Lena. He has to think the man he grabs is a potential victim. Obviously, he wants to keep him quiet, but there's no reason for Hank to hold his gun against an innocent man with his finger on (or near) the trigger.
Other mistake: In the final scene Hank walks away in the opposite direction to the exit and walks around a corner that goes nowhere. This is confirmed from an earlier scene when the thugs broke in to the apartment and they enter the hallway from the opposite end. (00:42:00)
Other mistake: It is right after dinner when Angelina and Nick leave for the bar, but when they get there it's daytime.