I've canged my cache folder to 755 but I find that when I later went to the site the galleries were again not appearing. The debug reported the files themselves were unwriteable. I found I have to change the permissions for the individual jpg files stored in the cache to 646. Why doesn't this work automatically?

It has to do with your server and what file permissions has for this folder that your whole site is in. What permissions does it give when files/folders are created, etc.

I am not sure but seemed to have solved the problem with 777 for the cache and 646 for the files. Isn't it a security problem to have 777 for the cache?

I am not sure but seemed to have solved the problem with 777 for the cache and 646 for the files. Isn't it a security problem to have 777 for the cache?

Yes it is a security problem. Anytime you change the permissions to 777 on anything it is almost always invariably incorrect.

The web server itself needs write perms for the files in the cache (jwsigpro v1.2 didn't require this). Which leads to:
Advice given to change the directory or the files to 777 is going to "work" but it is over compensating for the issue and is the incorrect answer.