When Monica is serving cheesecake to Pete in the diner she places the lid to the cheesecake display case back over the cheesecake. After this the lid disappears and reappears multiple times.
When Chandler enters the girls' apartment, he states that he had forgot the combination for his briefcase. However, when he recognizes Pete's name, he opens the briefcase and takes out a magazine.
At the diner when Pete is asking Monica out, the amount of cake pieces behind Monica changes between shots. Also Monica puts a lid on them and suddenly it has disappeared.
In the diner scene, Rachel makes the comment about working in fashion and straight men, and her left hand is empty; in a flash, a piece of bread appears without her picking it up.
While in the diner with Rachel, Monica makes a comment that she had only gone out with two guys, Richard and Julio, but in "The One Where Ross and Rachel Take a Break" Monica goes out on a date with the interpreter Mischa.
When Pete turns off the last of the three video screens with his remote, the screen goes blank just before he points the remote at the screen.
When Pete comes to the door to pick up Monica and everyone gathers around to see him, the top of the set, including lights, etc, is visible.
Given the differences in time zones and the time it takes to fly to Italy, it would be morning time by the time Pete and Monica made it to the restaurant.
When Pete first arrives to pick up Monica for their date, Rachel excitingly says "oh my god, the millionaire is here" when in fact Pete is a billionaire.