There are some extremely minor errors, such as Sisko and Jadzia working at a panel that wasn't there on the original show, or Kirk's conversation over the intercom being several seconds longer than it should be, but I honestly can't say that I give a damn about such things.
In the same vein the only slight-but-not-at-all-important issue I have with this episode is that they changed the sound effect of Kirk's chair intercom. In the original Tribbles episode it just goes 'click' when he calls sickbay. In the DS9 episode it goes "BLALALALALALALA!"
, and couldn't be more noticeable if it tried...