The whole point was that Jerry and the two cons were bumbling idiots. Add to that Jerry's desperation and you would expect some pretty absurd actions.
Actually, if you read about real life crime stories like this, the actions of Jerry aren't all that different. People like that are always doing shockingly stupid things that will ensure their capture. For example, I read The News of the Weird (a collection of hilarious stories from newspapers). Every year, they have a list of stories they will no longer feature because they have become too common. One of the stories that they stopped running last year (because there were too many of them) was stories about people robbing banks and getting caught because they signed their name on the "Put the money in the bag" note.