I am new on here.  I have a 1978 with a ZZ4 engine.  For showing, I had a Edelbrock endurashine intake manifold and matching endurashine carb installed.  The car is at the local Vette doctor as I type and he is trying to trouble shoot why it backfires.  The car backfires when it up to temperature and just cruising in town (30-45 mph).  The car doctor called me yesterday and told me that when the engine was swapped, the mechanic installed tapered thread plugs.  The standard ZZ4 cylinder heads are aluminum and require the old style straight thread plugs (oh...and of course they sell for $9 each compared to $2 each for the regular plugs...sheeeesh).  I am surprised that I did not blow one right out of the head.  They have been in there for 6-7 years!

Welcome to C3VR!! 
Lottsa things come to mind with a backfire, but a little more info is needed:
Does it backfire/pop thru the carb, or the exhaust?
Is it a constant backfire, or very random?
Did it do this before the intake/carb swap?
Does it start and idle ok?

If this problem only started after the swap, my first thought would be a lean carb mixture. It could also be that one(or both) of the intake gaskets slid out of place, and is now just a vacuum leak source. Could also be the timing, but, from the description, I would think it will probably be something causing a lean fuel situation. Your "Doctor" should be able to read the plugs, even if they are the wrong ones, and see if it appears to be running lean, or if only one or two are lean.
Might just give the guy a little time, and see what he comes up with.

Thanks fort he input Adam.  We had a cat JUST like the one in your photgraph....he just showed up one day and we named him Casper. 

i thought there was a fairly common burnt exhaust valve problem with stock zz4's

Thank you CT..I will pass that along.  The mechanic is also replace the valve covers at this time, so he can easily check that as well!

I never had any problem with backfiring with my ZZ4. Good luck with it, I hope they get it worked out for you.

I never had any problems with my ZZ4 with an Edelbrock carb. Ran fine and had plenty of power. Actually had more power than with the Holley 750 that was on it originally. If the tech can not find the cause of the backfire maybe it is time for a new tech. I know of mechanics with lots of years of experience that can not do any more than change parts until the problem goes away.

The backfiring occurs when you are slowing and pull the trans into a lower gear. This will cause a rich condition and there is a hot spot in your exhaust that is igniting the fuel in the pipes/mufflers. Usually there is not enough oxygen in the exhaust system to promote burning so look for an exhaust leak allowing O2 to enter the pipes.

With the complete description of the problem now, I agree with Phillip...you prolly have an exhaust leak, most likely somewhere up around the junction where the pipe meets the manifold. If you still have the AIR system on the car, check all of that, too...a leak in the tubes, or a bad diverter valve can also add more O2 to the exhaust stream, and cause a backfire on decell...

Thanks Philip.  That was good information.  I had wondered why the popping was way back by the mufflers.  That is probably where the 'hot spot' is.  This mechanic did tell me that he would check the exhaust system for leaks.  I was also VERY pleased to read that you have had GOOD luck with an Edelbrock vs the Holley.  That gives me hope.  Again, you ARE right about your assement about mechanincs.  I have HAD (past tense) one of those too.  He was VERY good at re-building engines though!

Adam,