When Max pretends to be 'Olga', judging by her accent and name, she is supposed to be Russian; at one point she addresses Tensey as 'Babooshka' in an affectionate tone. When in fact 'Babooshka' is Russian for Grandmother. However, a plausible excuse for this would be that Max was unaware of its actual meaning.
When Jack joins Max in her hotel room she intentionally leaves the door slightly open (in order for Page to be able to enter later), but when Jack wants to leave a little while later, the door is suddenly closed.
At the auction, Tinsey stops just inside the door to look at a statue. While standing there, a couple comes in the door, passing him on his right (the woman is wearing a black and white print dress). Although the couple walked completely past him, the next shot shows a close up of his face, and the same couple is back at the door, coming in again.
When Jack takes Jane into their honeymoon suite, the door closes behind them without anyone closing it. In the corner, if you watch the doorknob, there is a hand that you can see that closes the door for them.
When Dean Cumanno gets on Jack Withrowe's boat he shoots his gun off into the water but there is no recoil, muzzle flash or smoke from the gun and there are no indications the bullets are hitting the water.