Question: I've attached some JPG files to notes in contact records, but them I can't open them and if I save them locally then most applications can't open teh saved version and say they aren't in a supported file format, though surprising, Adobe Acrobat will open them (which is not a solution for most users).

I'm using WordPress 5.3, CiviCRM 5.15.1

Any ideas what could be going on?

Answer: 
Eventually I found out what the problem is and it is caused by the child theme that I had created. Another problem elsewhere that had an extra blank line at the start of a news feed and Demerit's comment above suggested this as a solution. When I changed to the base theme all was fine. Going back to functions.php for the child theme I found a blank line outside (though not at the start of the file which is why Demerit's suggestion didn't lead me to the solution before).
Do you have Shoreditch theme installed? This will complicate a few things in WordPress and even the fabulous CiviCRM Admin Utilities WP-Plugin won't fix it.

Try this extension from bgm: <https://civicrm.org/extensions/shoreditch-wordpress-workarounds>