When installing add-ons using the functionality as described on http://docs.moodle.org/25/en/admin/tool/installaddon/index it is possible that when the files are copied from the 'moodledata' folder to the moodle installation folder the wrong permissions are used thus causing a 500 internal server error on a Unix / Linux operating system when the plugin is used.

If a plugin is unzipped locally and FTP'd then the issue does not occur.

After extensive investigation (and from other sources) on: https://moodle.org/mod/forum/discuss.php?d=238274. I have discovered that the folders are being copied with a '777' permission and the files '666' and that manually correcting this recursively for folders to '755' and files to '644' rectifies the issue.

It might be that there is no actual code fix but rather improved instructions to set the permissions on the 'moodledata' folder as '755' for folders and '644' for files ensuring the owner and group are the same as the web server.