To allow other than images uploads in comments across the site (except discussions) run the following query:
UPDATE `sys_objects_storage` SET `ext_allow` = 'jpg,jpeg,jpe,gif,png,pdf,zip' WHERE `object` = 'sys_cmts_images';
In above example pdf and zip file types were added, but other extensions can be added there as well.
Please note that preview is generated for image files only, video and audio files will not have preview.