I'd really like to take my Dom built golf ball size Thunder Mug along with me when going back to Illinois to visit my kids. Have a son down in the Peoria area and I know he'd appreciate having this little thing going off in his back yard. I'd really prefer NOT to have him asking the local law enforcement folks about this as that'd be like turning himself in.....JayAK please be sure to let us know what you finally find out about shooting BP martars and cannon in that "wonderful liberal" State of Illinois with it's stupid STUPID firearms laws. 
I have looked over the Illinois state firearms laws....and there is nothing that I can see about cannons etc....they do however consider all muzzle loaders/black powder devices "firearms" thus you must have a FOID card if you are an IL resident....you must also have
either the gun or the ammunition cased... so don't go driving in with the mortar in the back seat with a cardboard box filled with powder and balls....that would be a felony by the standards listed on the IL state police site.....
The only other issues that I could see coming up are noise/sound issues/ord. if you are in town...
ORspecific local ordinances against firearms....
here is a link to those...
http://www.isp.state.il.us/foid/ordinances.cfmThere are ordinances posted by town/city on the right side.....
I am not a lawyer....
So good luck!