Sync problems between audio and video in iMovie have gotten significant discussion on the Web. After one individual had almost completed his 40-minute video project, he reviewed it in the iMovie browser. When he was satisfied with his editing, he exported the video. However, the exported video file had a significant problem: the video and the audio were out of sync.
That's really a problem when you have tight shots of people talking.
We have run into this same problem several times. We tried everything from exporting the video in different formats to deleting all the video transitions, to no avail. Simply put, the words were still not moving directly in-line with the person's mouth.
This problem found with certain iMovie editions seems to have a relatively simple, although still slightly annoying, solution. Simply click on each specific clip and separate the audio from the video, by clicking on "Detach Audio".