It could be that the format of the avi you're importing isn't quite right for Premier. I've been having the same problem with avis recorded on my Canon Ixus 50. It seems (and someone else will probably know more than me) that the AVI file format isn't so much a file format as a 'wrapper' for other types of file. And, it turns out, AVI files aren't the same as DV AVI files - This, it seems, is the format that Premier recognises and can work with.
The way round for me was to download the free version of STOIK Video Convertor 2 and convert my AVI files to DV AVI files. It's a bit of a faff, but it seems to work. Or you could use Windows Movie Maker to do the same thing, I think...
Not that I've worked with mov files, but can't Premier import them directly? Or does it do the same thing with them?
Hope that helps.
Mark
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premier problem video plays in monitor but not in sequence 
Linear Mode
