Can I move an existing iPhoto library to a location on a network-drive so I can use it from multiple apple computers?

How do I do that? (including what I need to do to iPhoto on all my apple computers) Are there any disadvantages?

You can do it, but do it with caution. I've run network home directories before, which is essentially what you're describing, and iPhoto supports it fine. On your standard Desktop OS, simply create alias to the iPhoto library on your network share in your User home directory photos folder. You can also set iPhoto to use a new library in a new location by opening iPhoto with Option (Alt) held down, where it will then prompt you to locate the new library (which would be on your network share).

The biggest issue you'll have to address is ensuring it's not open and being edited by two iPhoto instances at the same time. I'm not 100% sure how it will behave, but you can bet not well. You could get situations where photos become orphaned, etc.

You should note that iPhoto needs to have the Library sitting on disk formatted Mac OS Extended (Journaled). Users with the Library sitting on disks otherwise formatted regularly report issues including, but not limited to, importing, saving edits and sharing the photos.

Recent versions of iPhoto will not allow you to move or create a library on a NAS.

Workaround: Put the library on a Disk Image formatted Mac OS Extended (Journaled) and store that on the NAS