Since there are two major factors that may lead to QuickTime won't open MP4 files - MP4 file quality and QuickTime MP4 codec, to go on with the following first three solutions, you should in advance check the media info or try playing it on other MP4 players like 5KPlayer, VLC, KMplayer etc to make sure that the MP4 files playing in QuickTime are complete without damage.
Solution 1: QuickTime Player Upgrade for MP4 Codec
If you find your QuickTime fails to open MP4 files, check immediately whether you have the latest version of QuickTime player for MP4 playback. For the most part, QuickTime 7 and above can handle MP4 files well and even other formats beyond. So, make sure if you've got the QuickTime upgraded in time. Note that QuickTime 7 pro are not free. So you may have to spend some money, about $29.99 USD for the upgrade.
Solution 2: Download QuickTime MP4 Codec Pack
If you still cannot play MP4 videos on QuickTime, chances are that the MP4 video/audio codec is not supported by QuickTime built-in codec pack. You can go to Softonic or CENT to get QuickTime MP4 codec pack downloaded as a supplementary. Be aware, we do not fully recommend this approach since it might bring along adware/malware and is not 100% safe for your computer, the reasons of which have been illustrated in Downloading VLC Codec Packs.
Solution 3: Video Converter –Convert MP4 into QuickTime Supported Format
Directly converting the MP4 videos into MOV or other files formats that QuickTime can handle is one of the most convenient way to avoid QuickTime not playing MP4 problem. If you are not sure about the target converting format, you can test a certain video format that can be played by your QuickTime to decide. Here, we recommend you some professional converters you might be fond of: WinX/MacX video converter; Any video converter; Handbrake, Freemake Video Converter.
For more info, you can visit:
Top 3 Online Video Converters
Top Free Video Converters for Mac
Solution 4: MP4 QuickTime Player Alternative –5KPlayer
Note that there are several formats that use the ".mp4" file extension, including those that are proprietary to Microsoft, that have not been ported to Mac. If you just want to play the MP4 video any way you can, and don't particularly need it in QuickTime, you can try the free HD media player –5KPlayer which supports more formats and is able to play incomplete, unfinished, damaged videos or an unknown format in its raw form, which is a better solution to QuickTime not playing MP4. 5KPlayer also outshines other MP4 players in image rendering and 4K/8K video support, including HEVC H.264/265, VP8/9 etc. Other file formats like FLV, WMV, MKV are also supported by 5KPlayer.