The "Video Rotate" app from Gadget Juice is just what I've been looking for! It allows you to do a frame-by-frame reencode of movies on your iPhone adjusting for a specified rotation. This is useful if you accidently switch rotations during recording, but is also useful for rencoding the video so it can be played back in VLC and other non-Apple players with the proper rotation.
When you first open the app it will ask for permission to access your photo library. Once you grant that access, you can see your recorded videos in a list. Tap on the video you wish to modify.
The app detected that my video already had a meta tag saying the rotation should be 90°. Even though it was already selected, I tapped on 90° and was prompted to choose a rotation mode.
Choose "Slow" mode to re-encode your video.
On my iPhone 5s I was averaging around mid-fifties for re-encoding framerate. Not bad! My wife's iPhone averages in the mid-thirties. This sort of heavy lifting really shows how a 64 bit architecture improves performance.
Once done your new movie (complete with a new filename) is added back into your library.
My original movie was 27.3 MB. After the reencoding it was 34.7MB. I didn't notice any degradation in quality. Keep in mind at this point it is still a 1080p video. I like to save my files in 720p to save on storage space. I shared the new movie with my mac via iMessage (send an iMessage to yourself from the iPhone with the Messages app open on the mac) and it came across as a 3.7 MB 720p video. I haven't spent much time comparing the quality of the iMessage encode to that of Handbrake, but my guess is handbrake is much better so I will continue to use it. By the way, did you know the Handbrake app can do batch? Just add an entire folder to Handbrake, it will scan each movie as a separate title. In the File menu you'll see there is a new "Add All Titles To Queue" option :-D