Backfiring is either a valve stuck open or a lean mixture or spark plug wire(s) connected to the wrong cylinder(s). Check compression on all cylinders and then look for vacuum hoses loose, cracked, misconnected. Check the line for the vapor recirculation system – it is easy to knock loose and not see it when you connect the air pump plumbing. If the vacuum line for the EGR valve and the air pump are cross connected, some very strange things can happen. Check the mass air flow electrical connection and see that it is tight, the same goes for the fuel injection wiring harness connectors up on top of the manifold near the firewall.
Dump the codes and see what the computer says is wrong…
Here's the link to dump the computer codes with only a jumper wire or paper clip and the check engine light, or test light or voltmeter. I’ve used it for years, and it works great.
See
http://www.troublecodes.net/Ford/
OR
See
http://www.mustangworks.com/articles/electronics/eec-iv_codes.html
IF your car is an 86-88 stang, you'll have to use the test lamp or voltmeter method. There is no functional check engine light on the 86-88's except possibly the Cali Mass Air cars.
Codes have different answers if the engine is running from the answers that it has when the engine isn't running. It helps a lot to know if you had the engine running when you ran the test.
Trouble codes are either 2 digit or 3 digit, there are no cars that use both 2 digit codes and 3 digit codes.
For those who are intimidated by all the wires & connections, see
http://www.actron.com/product_detail.php?pid=16153 for what a typical hand scanner looks like. Normal retail price is about $30 or so at AutoZone or Walmart.
Or for a nicer scanner see
http://www.midwayautosupply.com/detailedproductdescription.asp?3829 – It has a 3 digit LCD display so that you don’t have to count flashes or beeps.. Cost is $35.