Can't see all images in media library after moving website

When you move a site, you must replace the old URLs and paths with the new ones. Some of these are stored in the database in ‘serialized’ form where the string length is stored along with the string. You must use special tools to search and replace the old values with the new ones.

If you replace an old URL with a new one of a different length, it will break the serialization, causing many different problems.

If the old site is still available, you can use the steps shown in this article to copy the site: http://wordpress.mcdspot.com/2012/08/22/migrating-a-wordpress-site-step-by-step/

If the old site is not available, and you still have a copy of the database from that site, you should be able to use this tool to make the changes: http://interconnectit.com/products/search-and-replace-for-wordpress-databases/