If your mp4 has strange crossover between frames, you may have run into a bug with the Windows mp4 exporter.

This sometimes happens when the frame rate is 15fps or slower.

To resolve the issue, in the Export Movie dialog, check the box to “Convert frame rate in output”, and set the output frame rate to double the natural frame rate.

For example, if you were seeing issues at 12fps, you export with an output frame rate of 24fps (leaving the source at 12fps).
The end result is that each source frame is doubled in the export. It will look exactly the same, except it should get rid of artifacts in the output.