Grace says the vault code changes daily, but the code is the same, both when she shows Neal and the next day at the wine tasting.
Peter's grip on his wine glass changes between shots. He also raises his glass to his lips twice.
When Neal opens his door for Peter, Peter's head is tilted up and he's biting into a slice of pizza. After the cut his head is level and his pizza hand is down.
When Peter interviews Sir Roland Cattigan and calls him Mr Cattigan, he is corrected and told the name is Sir Roland Cattigan. Peter then addresses him as Sir Cattigan. A real Knight of the Realm or possibly a Baronet (it is unclear but the character is more likely to be a Knight) would be addressed as Sir Roland and would have again corrected Peter.
The body text of all the newspaper clippings on Neal's desk, about the museum robbery, is identical despite supposedly having different authors and being cut from different newspapers.