Considering the 2000 LS was the first model, Lincoln got all the first year production items pretty much hammered out in the 2001 model. I have a 2001 LS and the only problems I had with mine were the hard starting issue (fix two leaky injectors) and the A/C controller went out. Other than that it's been a very dependable car at 81,000 miles. I will have to replace the valve cover gaskets soon since it just started leaking. This was a common problem on several LS's but Ford upgraded the gaskets and once replaced with the new gaskets leaking will not occur again.
There are well documented issues with the LS on this site. Look throught the LS forum and you'll see some items that can be fixed rather easily. You'll find a lot of great information on here but do a search if you can because more than likely your question has been answered in another thread.
BTW, Welcome to LvC!