Unsure quite how knowledgeable on Omegas you are, and any car bought off here won't be hiding the below issues but... just as a mini-Omega-guide, HG failure tends to be a mostly 2.2 issue, the V6 tend to suffer from oil cooler failure (often mis-diagnosed as HG) both are jobs which can eat a couple of hundred, as I'm sure you know.
As a general rule Omegas to keep running well will want their timing (V6) doing and front suspension followed by a full geo setup (all models) which, again, can swallow a couple of hundred. Uneven tyre wear is common on them, and so looking at the rubber will help determine if they're setup poorly (as they 90% are)
Everything else, exhaust, rust, brakes etc apply as with any car, though Omjegas aren't very rusty cars at all, as they have plenty of rustproofing measures.
There's a host of niggly things which can go, but these are all easily sortable, and most likiely you'll inquire, expecting horrible expense, only to find the issue is actually a very cheap/free fix.
Oh, watch out for water in the passenger footwell - it's (probably) not a knacked heater matrix, but leaves and rubbish blocking the scuttle = free fix.