During the scene when Antonio Banderas is talking to Radha Mitchell at the Russian night club at around 26 minutes the mark, there is a techno remix of the traditional Russian folk song, "Korobeiniki". "Korobeiniki" is also the theme song for the Nintendo classic puzzle video game, "Tetris"
When Ripley (Morgan Freeman) and Gabriel (Antonio Banderas) are talking on the rooftop you can easily see in Gabriel's sunglasses the microphone and the cameras.
(at around 40 mins) When Martin (Antonio Banderas) and Ripley (Morgan Freeman) are in the subway together and Martin takes out the iPhone to mark the spot on the wall, you can see by pausing the movie that he just clicks on the Photo application and then the lock room's plant suddenly pops up out.
An ultrasound transducer was placed in the first Vault in order to block the sensors but when the second Vault is open it can be seen behind them that the transducer is missing.