Having a lot of links from a facebook page probably won't cause a penalty. I haven't checked this lately, but I thought that the facebook scripts automatically put a nofollow tag on all outgoing links anyway.
You didn't say whether you're sending all the links to the same page on your site or to different pages. Sending them to different pages would probably be better.
But taking everything into consideration, any new links you add in the future will probably have little if any effect on your site's rankings. Most likely the only benefit from them would be traffic.