The MP4 container is somehow broken actually (see ticket
#2715) and the result is files with a strange behaviour with video playing faster than the nominal framerate and being out of sync with the audio.
At this point you have two options:
Demux and remux your MP4 file with MP4Box (a part of the
GPAC project) to obtain a new working MP4 container.
On Windows this can be easily done with
YAMB as a GUI. Latest binary of MP4Box for Windows can be found
here.
Or convert your AVI to MP4 by using another tool such as
AviDemux.