The app itself is called Remo Repair MOV and not "MP4 Video Repair Utility". But as it turns out, you can repair both MOV or MP4 videos. Or can you(?) Remo Repair MOV has a sister application called Remo Repair AVI, but that's not on our menu today.
Remo Repair MOV doesn't just work like magic. Although it's barely mentioned on the official product page, the interface itself clearly suggests that you need a source file in order to restore the corrupted file back to health. Now, I wonder, if I had a an un-corrupted version of the file, why would I want to repair the corrupted one? If I have learned one thing while fiddling with my dad's computer in 1994, it was that copying is a valid option to replace missing or corrupted files. This Healthy vs Corrupted thing makes almost no sense to me. Let's say though that the file is too big and it would take too long just to copy it over the corrupted one. Let's say the police is to arrive at any moment or something. It would then make sense just to read both files and mirror the changes to the corrupted file. I suppose that would take less than one read and write. But that doesn't mean you need the exact original. Maybe any file that has the same format and codec is good for the job, I suppose.
So I searched the Interwebz for MOV files. I have found some small ones (less than a meg). After creating a copy, I've opened one in Notepad and scrambled the code a bit. I then put Remo Repair to work... 'Hmm... Unsupported file format' it read. 'Well maybe I need a video that was created within this decade'. So I downloaded a 100 mb video. However now I also had to get a hex editor, because 100 megabytes are bit too much for Notepad to handle. I finally changed some 65's to 00's and some 00's to ff's and the job was done. Launched Remo again... - Same error. Nothing happened.
Well, I can't say I didn't try. At least I got to play around with a hex editor. However Remo Repair is probably missing a code string or two. Maybe the installer itself is corrupted. Who knows. For now, just make sure you're not copying valuable videos while the cat is playing with the power cord.