In this episode, when Neal tells Mozzie that Diana is going back to work, Mozzie says that he never met his namesake (Diana's baby Teddy). But not only did Mozzie delivery the baby, but he was at the hospital with everyone else at the end of episode 5.2 (Out of the Frying Pan) with the rest of the cast. In the scene, Diana is holding Mozzie as she was laying in the hospital bed.
When neal is handed the file he does not life the top page up but in the next scene it is lifted up.
The "algorithm" shown on the computer screen is code for drawing on an HTML5 canvas.
Peter and Neal bag vast amounts of evidence without wearing* gloves, leaving false fingerprint evidence all over it. Additionally, Neal opens evidence bags by blowing int9 them, potentially leaving false DNA evidence.
I hate it when writers get lazy with their own characters. Given all we know about Mozzie over the last five series, we know that he would NEVER leave such information on a voicemail.