Can you please show the export settings that you are using? MOV with PNG encoding should not have a reduction in quality. It's not the same frame, but the colors are very different in your screenshot. Have you tried other players?
I have found some players fail to play a video which other players can play just fine, especially when the video is high resolution (eg larger than 1920x1080). I haven't been able to tell if it is the fault of the video codec or the players, but my guess would be the players.
There has never been an MP4 export, sorry, only AVI and MOV.