Well, there's one where initiating a Blockbuster Sequel (this game's name for DHCs) sometimes causes the incoming characters hitboxes to show for a few frames before launching their attack. Though, I've heard that Mike Z actually thinks the glitch is kind of cool-looking, so that might not be fixed in a later update.
The more prominent however (at least for me) is the sound glitches. On numerous occasions during the intro/outro voicework (and I think I've even experienced this during supers as well) will play the characters voice twice, one on top of the other. Sometimes it's the same line, sometimes it's two different lines, but it's pretty noticeable.
This seems to happen mostly online, from my experience.
And I know that they've already planned to support the game with DLC characters. The two ones that they've confirmed to do first (assuming they'll be able to work on them) are Squiggly and Umbrella. Other popular ones that will probably get attention sooner rather than later are Black Dahlia, Panzerfaust, Leduc, and Big Band.
http://wiki.shoryuken.com/Skullgirls