Meriweather was a key stomper in the Miami-FIU brawl this past season. Look for #19 in this video stomping on a FIU player. Moss is one of the best receiving talents in the NFL, but has a long list of controversies in his wake.
So, can the Patriots, with their well-documented focus on character, keep these players in line? Things worked out very well with Corey Dillon. He had always been a malcontent, but as a Patriot he was both a model citizen and strong performer. He set personal and team rushing records in his first season. His production dropped off as he aged in the last two years, and he was released/retired this offseason. But, worth a second round pick (although he probably didn't last as long as the Patriots would have liked.
It will be interesting to see if the Patriots core of high-character players can keep these guys in line. My guess is that they will. The lure of winning a championship and the peer pressure from the Patriots players is pretty powerful. A guy like Moss can ressurect his reputation with a strong season with good behavior.
Also, it seems that the Patriots are able to attract people who are willing to take 'below market' deals in order to come to the team. Both Dillon and Moss reportedly restructured their contracts to help faciliate a trade. Supposedly, the Patriots were the only team Moss was willing to do this for. This kind of built-in discount is a huge strategic advantage for the Patriots. Kudos to Kraft, Belichick and Pioli for getting this done!