I think the biggest problem was the 01 thru 04 lb7's with the injectors, other than than there really isnt any real problems. Everyone has different problems but not many wide spread problems!!! Transfer case oil pump rub is probally the next most common problem!!!
I had an 01 LB7 previous to my LLY that I have now and I did recieve a service recall for the injectors from GM. The recall basically said that if you did have problems with the injectors that they would refund you for the cost of the repair done at the dealership. My truck did have a slight surge at idle that would roll off and on, which I think was a sign of a bad injector but who knows. I put 80000 miles on that truck before I got the one I have know and never had any problems.