Depending upon how your host upgraded to PHP 5.3.4, they could have made other changes to their server settings as well.

That this doesn't sound to have been triggered by any changes you made, means that changes to the server configuration are the first place to look, and the error logs may give some clues as to what's tripping the errors.

For example (and it's only one possible example), if they've changed the security settings to tighten what permissions are allowed on files (e.g. from 777 to 755), files that worked fine previously may now trip these errors. But this is really something to work through with them.