For the later '03 and '04-'06 LSes, you really only need to watch out for the same things you'd watch out for in any used car. They don't really have any endemic issues like the 1st Gens exhibit.
In the 1st Gens and the early '03s, you have to look out for the COPs and misfires. The usual suspect in COP failure is oil leaking into the plug wells, which is a symptom of leaky valve cover gaskets. Of course, you really can't tell this without pulling one (or more) of the COPs; they don't leak enough outside the engine to be noticeable.
The COPs in the '03s have an "extended warranty" on them; If you'll look around, you'll find a thread about it from a few months ago, including the letters with the program details.
I'm sure the 1st Gen owners can tell you more about them...