After Helen leaves the FBI, Neal uses a magnet to move a penny up the outside of one of the shelves. Pennies are not magnetic.
The zip code in Amy Sawyer's address is different on the driver license (10014) and the employment eligibility verification (11148)
When Diana is entering her and Christie's apartment, she unlocks the door and pulls the door open. Entry doors to apartments, condos, homes, etc push in, not pull out.
During the dinner party double date attended by only Neal, Sara, Christie, and Diana, Neal asks Christie and Diana how they met. Diana doesn't want to tell or hear the story, so she gets up from the table. Sara says that she and Diana will get dessert. They head off to the kitchen start talking (Sara says, "I have to tell you, I love your place.") However, when Christie and Neal are walking into the living room, Sara is seen in the background clearing plates silently while her voice says "I love your place" to Diana in the kitchen. As their conversation continues (supposedly in the kitchen fetching dessert) Sara can clearly be seen in the mirror behind Christie and Neal still clearing the table, silently.