The Stadium - S1-E8
Deliberate mistake: The Korean lady's Mini-Uzi never runs out of ammunition, and she's spraying it at full-auto. A Min-Uzi's cyclic rate is 950 rounds/min. One long squeeze of the trigger and the weapon's dry. Same goes for all the other weapons like the M4 carbines being fired on full-auto, they have the infinity ammo cheat code going here.
Deliberate mistake: The ghosts often walk around furniture even though it was established that they can walk through solid objects.
Suggested correction: Just because they can walk through solid objects doesn't mean they have to. They were used to walking around things in life so just carry on doing so as a reflex action. They often use open doors too, only walking through walls when it's more convenient for them to do so or the doors are closed.
Deliberate mistake: In the restaurant after their daughter finishes talking to Niko, Erik turns the tablet device around and sets it on the table to talk to Niko. From his perspective, he is looking down at the screen. But in the other shots from Niko's perspective, where he is a life sized hologram, his figure is shown looking up and meeting her eyes. But from her perspective it should look like he's looking down at the table.