Although a "QT movie" video file with ".MOV" was recorded on an iPhone, my Macbook Air gives the following message: "QuickTime Player can't open "IMG_9358~video.MOV"." How can I fix the problem?

Newer iPhones can record in a format that isn’t supported by older OS X versions.

Using HEIF or HEVC media on Apple devices - Apple Support

The solution is to

• make new recordings in a more compatible format, so that those do not need conversion. On iPhone: Settings﹥Camera﹥Formats﹥Most Compatible
• convert existing videos to a more compatible format. This can be done during transfer. On iPhone: Settings﹥Photos [and videos]﹥Transfer to Mac or PC﹥Automatic. ‘Automatic’ refers to detecting the capabilities of the computer on the other side of the USB cable.

Agree with Urquhart - .MOV video file can be recorded with different compression codecs (e.g. h.264 or HEVC). The likely problem is that you've recorded the video file with a newer compression (HEVC), while your QuickTime Player doesn't support it. You may either convert HEVC to H.264, like Urquhart described this. Or use a video player that supports HEVC. For example, VLC is a free media player that supports most of the video file and compression types.

The other problem with the file could be that the video is not finalized (the file misses a header, which could be a result of some glitch). If this is the case, you won't be able to play it in ANY media player. In this case, you will have to use a .MOV repair tool. Here is a great article on how to fix .MOV files: https://restore.media/blog/repair-mov-file