Was watching the Lucio Fulci film House by the Cemetery last night. I certainly knew of its reputation as being a tad on the confusing side at times (and has a version released with scenes in the wrong order). Some scenes may be quite odd, but the one where the babysitter cleans up the trail of blood* is rather puzzling. So which films have parts to them where a scene just doesn't make sense. It should be understandable as to what is going on, just not fit any explanation. So a random plot development like the helicopter in Demoni wouldn't really count. *The basic outline of this plot for the record [result]the monster in the basement killed a vistor to the house whilst she was trapped in a broken gravestone in one of the rooms (and yes it is a relatively normal house too) before being dragged to the cellar leaving a huge bloodstain on the floor between the two points, including passing through the kitchen. The babysitter cleans this up, and has to this point seemed suspious, but turns out not to be. She is hard at work in the kitchen cleaning this up when the woman of the house turns up and asks what she is doing. "Making coffee". This appears to suffice, and the hole in the floor where the gravestone has noticeably broken isn't noted[/result]
The opening of Andre Rublev is famously inscrutable. It's also never clear how the kid in The Sixth Sense knows that his teacher used to stutter.
I realize it's a movie full of supernatural shenanigans, but the scene with the guy in the bear suit from The Shining is just out there.