The option "Show on screen" to limit the displayed number of elements is missing in the link-manager.
I know this option is also missing in all stable releases, but I thing it counts as bug, because every content-type (posts, media, pages, comments) offers this option except links.
It's not a bug -- the link manager simply doesn't have paging currently.
We'll probably be re-imagining links, in a near future release, as a custom post type. It'll receive paging automatically then.
In the meantime you're welcome to submit an enhancement on http://core.trac.wordpress.org.
Thanks!
Thanks for your quick response. I submitted an enhancement request.