Apart from blown head gaskets (which are common in all E-series Falcons) the EA is known for having poorly aligned panels and poor paint work. The EA introduced a new lineup of engines and was a new bodyshape and wheelbase. Expect your usual teething problems. The EA was a huge undertaking for Ford at the time.
Power steering leak
Loose drive belt
Split vacuum hoses
Inconsistent idle
Power window, power mirror and central locking issues
Blown headgasket
Warping front discs
Cracking cylinder heads
Water pump failure
Automatic transmission failures
Suspension bushes
Interior Electrics issues
Failing coil packs
Faulty fuel pump
Body panels misaligning
Poor paintwork