Missing and backfireing, while running - 2003 Harley Davidson FXDWG Dyna Wide Glide

First off, if by backfiring you mean that it is popping out of the exhaust, this is the result of the missing problem. When the enigne misfires, the unburned fuel/air mixture is exhausted into the exhaust pipes. The next time the engine fires on that cylinder, it ignites this unburned mixture causing the loud pop.

It sounds like your problem is ignition related. It the engine was starving for fuel, you probably would not have the backfire through the exhaust. The first thing to do is change the spark plugs. If you try to "test" the spark, you must have a set of plugs in the engine as your engine is equipped with a compression sensor. If there are no plugs in the spark plug holes, no compression, you will not get a spark. If the new plugs don't cure your problem, you probably need to take it to a dealer. The reason is that trouble shooting the electronic ignition is very difficult. Replacing parts until you fix the problem is very expensive. Regrettably, bikes are headed the same direction as cars, no user servicable parts on the machine. That's why I still ride a Shovelhead with points, a coil, and a carburetor. The EPA hates me too.