A lot of problem areas depend on what you're going to do with it. If you're going to rag on it practically everything is a potential problem (a few specifics are the rearend if it's still an R180, cooling, and probably the frame twisting from hard launches). Is it a standard or automatic and what model?
I would say that a carbureted 327 with HEI is a very dependable setup enginewise. A points type setup will probably be more maintainance (switch to HEI). Make sure it keeps good oil pressure especially when it's hot. Visually inspecting the oil for darkness and any contaminants and also smell it for gas or a burnt smell. Some would suggest a compression test which is not a bad idea but takes time. You can probably get a good idea how worn the engine is by driving it and seeing if it cruises or if you have to seemingly give it more gas than you think you should, driving it hard making sure it accelerates right and doesn't smoke, and listening to how long it takes the engine to stop when you turn it off. The rest of the drivetrain really depends on how you drive it if it checks out initially.
Have you not driven the car yet?! If it's not an overdrive tranny and it has the usual gears like a 3.54 or maybe even a 3.90 you will have a very high cruising rpm which will not make a good daily driver. Unless you're getting a REALLY good deal on it I would make sure you test drive it and inspect it very thoroughly for rust and the above problems, there are probably a few more problem areas that I haven't thought of but mostly you need to get a good feel of the cars condition and make sure the engine swap was done well. In the future please use the search function