Much is said about the looks and the sales effect the AU Falcon had. Dig a little deeper and you will actually find a relatively solid, reliable car. The biggest issues would have to be leaks of all kinds from the engine/ transmission and diff and blown head gaskets. It took nearly $700 million and nearly a decade to develop. The appearance has turned most second hand buyers off and in turn has sent prices down fast. If you can get past the looks you may be able to pick up a very solid reliable car at a next to nothing price. (I have heard numerous stories and even a first hand account of an AU Falcon that has been around the clock on a single engine without being opened up.)
Fluid leaks: Oil, coolant, powersteering fluid, brake fluid.
Transmission issues
Leaking diff
Worn drive belt tensioners
Blown head gaskets
Cooling system problems
The best way to accurately identify electrical and mechanical faults in a modern (mid 90’s onwards) car is to use an OBD2 scanner