I think this makes sense if there's a semi-nested structure to the discussion and the 'like'ing promotes popular posts to a more prominent position (like slashdot's system, which is really pretty similar to the facebook system though the organisation is different) but I don't see what sense it makes when applied to an essentially flat structure as we have here. I'd rather see a reply with :D or (nod) or "I agree.".
But yeah, wouldn't do any harm either other than possibly reducing the number of posts, as Ant says.
But yeah, if there's 'like' I'd really want 'dislike' too.
Perhaps have a user setting for the likes of Ken who are squeamish about dragon cocks, for them the font size of the post in question could be increased or decreased by 1 for each like/dislike the post receives.
If I was going to add it, I'd do a up / down vote thing but rather than the promotion system Slashdot have, which I agree wouldn't really work with Beehive's threaded structure, I'd probably go with something like Eurogamer's comment system where you have a user definable threshold (which would be a combination of total score and number of votes) and if the score goes below this the posts are hidden. Kinda like a social ignore list.
(This of course would be optional and you could choose not to set a threshold)