Can you change an MOV to an MP4 without transcoding?

Solution 1:

You could do that with ffmpeg:

ffmpeg -i video.mov -vcodec copy -acodec copy video.mp4

This will just change containers, but obviously will only work with a codec that ffmpeg supports.

Edit: if you absolutely need a GUI, you could use Automator to create a Drag & Drop target, like this:

Automator