In Dumb and Dumber, Harry and Lloyd are initially living together, poor, when Lloyd grabs the briefcase full of money from Mary at the airport.

Later that night, there is a knock at the door and they fear it is a bill collector, specifically, a bill collector for their gas bill. They escape their apartment and leave a note for the "gas man," saying sorry and that they are going to Aspen.

The "gas man," the hired goon trying to track down the money, notes "these guys must be pros and following us for weeks. How did they know I had gas?"

A few scenes later, the "gas man" has a plan to get close to Harry and Lloyd by posing as a hitchhiker and thus the plot hole becomes apparent. Why would he hitchhike if he thinks that Harry and Lloyd are pros, have been following him, know who he is, etc?

Most likely, this plot hole came about by adding in the joke made by the gas man later, or it was resolved off screen when the gas man realized that Harry and Lloyd were actually just a couple morons--but it seems like he doesn't really realize this until minutes before he dies, so this might be a legitimate plot hole in an otherwise stellar movie.