There is a nice weekly podcast that I listen to called All Movie Talk. It's hosted by Stephen Keller and Sam Stoddard. They do a 1 hour show once a week and do a top 6 list of films that have a particular characteristic or genre as well spotlights on directors or film genres and lots more.
It's a great podcast and you can subscribe to it on iTunes or check out their site HERE.
In the last episode, the top 6 lists were on great films that have gaping plot holes in them A couple of gems from this list were:
The Big Sleep - The chauffeur is killed but we never find out who did it. In fact, Howard Hawks called Raymond Chandler (the author of the story) up and asked him and he allegedly said "How the hell should I know?".
Citizen Kane - The film's premise is driven by a reporter who tries to discover what the meaning of Kane's last words were: "Rosebud". However, in the film when Kane dies and utters the famous "Rosebud" there is no one in the room to hear him say it. The nurse in the scene shows up after he has said it and has dropped the snow globe.
Casablanca - The plot device that drives the story here are the letters of transit. Once we get to the airport at the end, no one even uses the letters. They just get on the plane. Some other issues with the letters are pointed out in the podcast but you can check that out for yourself.