Using vaapih264enc gives erroneous DTS values, making the final mp4 file being played improperly in some non-linear video editors (like Final Cut Pro), with video-sound desync and/or black frames showing up.

A way to reproduce this is to run the following command:
gst-launch-1.0 videotestsrc num-buffers=250 ! vaapih264enc ! h264parse ! qtmux ! filesink location=test.mp4

Then try re-encoding the resulting file with ffmpeg:
ffmpeg -i ./test.mp4 -acodec copy -vcodec copy test-copy.mp4

Warnings of this kind will show up during the process (they do not show up using x264enc):

[mp4 @ 0xe557c0] Non-monotonous DTS in output stream 0:0; previous: 400, current: 400; changing to 401. This may result in incorrect timestamps in the output file.
[mp4 @ 0xe557c0] Non-monotonous DTS in output stream 0:0; previous: 12400, current: 12400; changing to 12401. This may result in incorrect timestamps in the output file.
[mp4 @ 0xe557c0] Non-monotonous DTS in output stream 0:0; previous: 24400, current: 24400; changing to 24401. This may result in incorrect timestamps in the output file.
[mp4 @ 0xe557c0] Non-monotonous DTS in output stream 0:0; previous: 36400, current: 36400; changing to 36401. This may result in incorrect timestamps in the output file.

[...]

Removing h264parse or using mp4mux instead of qtmux does not affect the output.