Quite possibly yes. File/folder permissions can be dicey. Set them too relaxed and the security software on your site may refuse to run scripts.You can probably fix the permissions with FTP, though.
It may well be that your site is simply mis-configured for an application like Zenphoto. Basically Zenphoto has to be able to read/write files and folders that it "owns". Strict permissions should work for that.
If the "user" that FTP runs under is different from the "user" that your CGI scripts run under you will constantly have permissions issues since Zenphoto will not be the owner of the newly uploaded items.