Mechanically, those cars were pretty solid (they convertibles are a pretty stiff ride though). I heard some of the auto cars has problems with DOD lifters, but if you get a manual the LS3 was pretty bug free by then. But I have to be honest here - the tops on the 2011's had a lot of issues. I owned my 2012 2SS vert since new and had to have the top replaced right at 35000 miles (a spot rubbed through). The 2011 cars were even worse - there was a recall that they performed that made them better, but even that couldn't get them back to what I would consider good. I think you have to figure a top replacement in if you are going to put significant miles on it. But if you just plan on having it out on sunny weekends, it will probably be fine.
-Geoff