I guess the question is whether Tweets are copyrightable?  Mark Cuban is ticked off because his tweets were republished in a newspaper or magazine (or in ESPN).  I'm not sure if these are the same tweets which cost Mr. Cuban $25,000 in a fine to the NBA.

Either way, there's likely little recourse here I'm sorry to say.*  Well, there is: STTU.  If Mr. Cuban approached me on this I'd say "save your money and energy."  There's little to gain by pushing this hopeless legal claim.  You risk looking like a bully, and worse yet, someone who is unsophisticated about social media.  Let me put it this way, I'd much rather be the dude who gets the call from the person who receives your cease and desist letter. 

* (There's no way in heck - even if you are a famed haiku writer - that an individual tweet is copyrightable.  The chances are probably even less in the case of a Tweet sent by Mr. Cuban in the heat of a game.  A collection of tweets maybe.  Even if an individual tweet is, a person who reproduces it can make a fair use/implied license (and probably other) arguments for why the republication (or Retweet) was appropriate.  Finally, if you haven't registered (or haven't w/in 3 months of publication), your damages will be minimal at best.  I guess if they took a screenshot of your tweet or published your photo you could somehow cobble together a claim through these facts?) 

NB: here's a post by Evan Brown that touches on this w/reference to Twitter's terms of service.

Added:  some clarification in the comments.  There's no length requirement or quantity requirement.  Here's a good post by Jonathan Bailey that talks about the issues.