Looking to get a 5th gen gtp . What are the common issues ??

So 1988-1996 ?

Age.

OBD1.x 1988-1995 difficult to troubleshoot depending on skillset and equipment available.

Gadgety buttons all over that can't be fixed or replaced because nobody knows how and whatever parts are available are also the same age.

Headliner falling down

Check tie rod ends

Depending on engine'* condition: head gaskets.

Depending on what engine yours has: ignition coils might act up

Depending on transmission'* condition: transmission problems

Depending on vehicle'* history of region: Rust around rear shock towers

Put a good fuel pump in it no matter how new the seller says the current one is, unless they can show receipts from a reputable shop (this will make inevitable troubleshooting much easier)

Put factory-spec spark plugs in it no matter how new the seller says the current ones are, unless they can show receipts from a reputable shop (this will make inevitable troubleshooting much easier)

Put factory-spec spark plug wires in it no matter how new the seller says the current ones are, unless they can show receipts from a reputable shop (this will make inevitable troubleshooting much easier)

Disclaimer: The list sounds ominous. The ask was for common issues. To all that are reading this, these can be good cars, but many got beaten from day one.

As said, OBD 1 is a bit harder to track down issues, OBD 1.5 reigned in the 1994-1995 years.

Also, the 3.4 DOHC is a COMPLETE nightmare from an accessibility standpoint.

In addition to others, Alternator failures and check the timing belt and idlers regardless of miles, due to age. the oil pump drive o-ring would leak oil down the rear of the engine and would require head removal unless one would get "creative"