The biggest issue your probably need to be aware of is rust and leaks due to incorrect roof rack installation. Although we don't have official word it appears that Novemberish Avalanches and on are having the roof racks put on at the factory now.
The problem is two fold. If the dealer just brushes aside the metal shavings from drilling to install the roof rack, they get caught between the weather stripping and the roof. These shavings then rust. What you do is open up your door, stand on the running board/kick plate and roll the weather stripping back at the roof. No rust your golden - rust let the dealer know! Mitigation has included cleaning up - in a couple of severe cases owners have reported the entire roof repainted and a couple have swapped trucks (at delivery or pre-delivery).
The second issue with roof racks is the holes are drilled to deep. What happens then is the water gets into the C and B panels and it appears your midgate is leaking. The reality is the water is coming through the roof. These two complaints are by far the biggest issue you need to watch for.
Midgate leaks are far less common but do happen. Alignment issues and gasket replacements almost always solve the problem. A couple of owners (heavy emphasis on a couple) have had problems with the installation of the water management system itself - again it was replaced. A couple of owners have reported severe problems resulting in vehicle replacement. Best way to test for this one is drive through a high pressure car wash, watch for leaks and fold the rear seats forward so you can completely check the floor. No damp - no leaks.
The next problem was a big issue on Avalanches born before 10/01 - although there have been a handful problems reported on Avalanches post 10/01 (ahhh, but when was the motor built). The problem is with excess oil consumption. If your Avalanche is burning oil you may need to replace the PCV valve (well document). More severe cases have required slides and lifters to be changed out. A couple of owners have reported swapping entire Avalanches and engines. This was a signifigant problem in 2001 and has largely been corrected (and is nothing of the scope of the Ford 5.4 liter leaking head gasket issue).
To aid in preventing this problem you should follow the break-in procedure - not that this is a guarantee policy but it gives you ammo for dealing with the dealer (most have had positive experiences but a few bad apples exist).
Front differential issues are not a major problem and there is no TSB on this issue. Only one or two people here have posted about differential issues.
Again, rolling back that weather stripping and a trip through a high pressure touchless carwash should answer most of your concerns right off the back. Please note that dampness and condensation UNDER the bed mat is quite normal. Also water appearing to be going down the inside of the tailgate is quite normal. When you open the tailgate the seal between the third panel and the tailgate is broken, and water sitting on top of the seal will come down and look like tiny streaks of fresh wet water when you open your tailgate.
Hope this helps!
