Can anybody tell me the most common cause of a severe backfire/poor running in these gas engines?

timing issues

Would you say the timing issues are most commonly in the ignitions or the engines?

No, but so is backfire.
Backfire is cause by lean mixtures and (combined with) late ignition, so take your pick. My Douglass Dragonfly motorcycle had an ignition timing manette, and could be made to backfire at will, much to my liking, though the neighbors did not.
Kickback is caused by early ignition timing, or failure of the electronics inside the ignition to retard the spark properly.

Thanks. A few weeks ago my BME began to run very rough with a slight backfire. Assuming that I had a bad plug I landed and changed plugs. Long story short I ended up pulling off the carb to find that one of my reeds were broke. Thinking I found the problem, I ordered and installed new reeds. Today I tried to start it up and the backfiring was still there. I am figuring that whatever caused the backfire is what broke the reeds in the first place? Anyhow, I will start by sending in the ignition.

Try checking the timing before you tear the ignition off.

a faulty ignition can do that.
Like Tim said, check the timing first.

I had a 3W backfire at high revs and it turned out to be the hall sensor.
sam

Check the hall sensor wires. Mine backfired when the wires started chaffing on the cylinder head.

I had a bad hall sensor on a 50cc.It ran errratically,timing was all over the place,including kickback and backfiring,it would run ok for a minute then go nuts and surge.
could also be ignition,a short,bad plug and wire,switch,timing,battery,ground.