Another 2005'er!
The typical GMT360 chassis issues are:
1) Engine cooling fan clutch. Supposedly updated mid 2005.
2) Weak waterpumps.
3) Weak power steering pumps.
4) Cheap ignition switches.
5) Wind noise from doors.
6) Cheap stabilizer bar end-links. All 4.
7) Clunky front suspension even with good end links.
8) Weather stripping and mouldings may need extra adheasive to stay in place.
9) Fuel economy that most owners complain about, but it's not different than any other same-class truck.
I'm sure there's more! Those aside, it's a great truck. Better than most domestics IMO, and a great used buy. I love my 2005, but only have 28Kmi on it. @ 56Kmi, at a minimum I'd change out the front and rear diff oils, then swap out the auto-trak II in the transfer case.
G/luck
Joel