When I replaced an old porch outlet with a GFCI the unit tripped as soon as I connected the downstream load wires.. There are no other outlets on the circuit, only a number of ceiling light fixtures in the two adjoining rooms. What should I look for? Also, is there any chance that an undetected ground fault could add to my electric bill over time?

There is no reason to have GFI protection for light fixtures, so the GFI should be connected that does not protect these lights.

There can be a accidental neutral ground connection in the downstream circuit causing the tripping.

Thanks for the reply. I know GFCI is not needed for lights... I just mentioned that for except one other outlet that tests "correct" the only other things on that circuit are ceiling lights/fans, one with a rheostat switch. Also, the wiring is old flexible metal bx without a ground wire. I assume the metal sheath provides grounding?

The metal sheathing of BX cable is allowed to be the equipment ground.

With those items, fans, lights, etc on a GFI circuit, clearly one has a ground fault.

This is an exterior receptacle and if the area is subject to water The GFCI is appropriate. TK is correct, your GFCI is doing its job, you have a fault somewhere.