Welcome to the Jayco forums.
There are many things to look out for, but the most expensive is to over look a water/moisture leak issue.
IMO find a safe way to get up on (or along side of) the roof and look for any rips, patching, etc., in the roofing material. If the Eagle has the Filon smooth outer finish, look for any signs of delamination (irregular rises, bubbles, etc., in the outer skin). Check for any surface irregularities under marker lights/windows. Also check for any brown stains running down from windows and/or seams (not the normal black streaks), this could be signs of moisture getting within the wall structure.
Check for "raised dimples" on the interior ceiling and wall surfaces, brown stain on counter-tops below windows, open all cabinets, pull/remove drawers, and look for any signs of moisture damage with a flashlight.
There is never a small leak, it's what's hidden that can cost thousands of dollars to repair.
Ask the dealer if there is any maintenance records with the TT.
I'm sure others will also offer other suggestions as well.