I'm buying an '88 Park Avenue with 34,600 original mile. What are some areas that I need to watch? Overall the car seems to be real solid with some cosmetic interior and exterior issues. Drivetrain seems to be flawless. I am obviously concerned what issues I might have from the car "sitting up". The a/c display is beginning to flicker with the entered temperature display fluctuating and the "off" button lighting up.Thanks for your help and time.

Welcome to the forums!
My father once owned an 88' Park Avenue as well. The biggest problems he had with it were problematic window regulators (particulary the driver's door, the window glass literally fell right inside the door)
If you have the automatic trunk lid pull-down feature, by all means do not slam the trunk shut! I learned this the hard way:)
The shocks and struts were all badly worn (originals with over 130k on them!)
The engine and tranny both performed flawlessly, smoother than my 92' PA!
You're lucky to find one with so few miles on the odo!