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MP4 files have been known to have these issues – usually just using MKVMerge to convert them to MKV (and checkmarking the “AAC” tab in the audio track properties) will fix it. If you do this be aware that the latest version of MKVMerge doesn’t work at the defaults with the Live – either use the older version (4.0 or earlier) or make sure you turn off video and audio header compression (also in track options).
MKV files as a rule don’t do this but if you are playing DTS and/or AC3 and decoding it (that is, setting the Live to “Digital” and passing through the audio to a receiver or television that decodes the track rather than selecting “Stereo” in the Audio/Video properties of the Live) you may well experience timing issues due to the nature of audio decoding. Usually receivers that decode have a delay feature which can adjust for this.
If this isn’t the case for you, please post how you are playing your files (complete information on your system setup) as well as the MediaInfo information for one of the troublesome videos.