A solution for syncing separately-recorded audio and video in older versions of iMovie. Newer versions (> 10.1) seem to work fine.
MPEG Streamclip is a powerful video conversion tool. It has not been updated to work flawlessly with newer versions of OS X. It does, however, convert video to Apple’s ProRes, video format, used widely across the industry, if you have downloaded and installed the Pro Video codecs. This conversion seems to avoid the iMovie audio/video sync bug. File > Export to QuickTime… > Options > Apple ProRes 422 LT