As for how to correct it, that depends on what type of sync problem you have. If the audio is out of sync by the same amount over the duration of the project, if the amount it is out is one fram (1/30 sec) or more, you may be able to adjust it in MEP. If it is less than 1 frame you are going to need to look at using an audio editor such as audacity (which is free) to make adjustments to the audio track .
If the sync gets worse or changes over time, that is a much more complex solution. I am assuming that you are certain that all specs between the original audio and video, frame rate, audio and video bit rates (data rates), sample rates, etc are the same.
Could you provide a little more detail on the type of audio sync problem you are having. I have been doing this for years but in order to help, I need more detail.
I'm back to the same issue. After a hell of a lot of fiddling and testing I've come to terms with the fact that MEP quite simply cannot export a Mjpg file and retain audio video sync. This might be a codec proble or a itrate problem, either way it's not working.
I'll keeping MEP for elementary work but unfortunately I do most of my production using motion jpg, so I'll have to start scouting for other software.