Is there any reason not to shoot a Riverside Arms 16 gauge single shot?

It depends alot on the barrel - very old shotguns may have a "damascus"barrel. To manufacture Damascus barrels, iron and steel ribbons were twisted together around a rod and heated in a forge (quick and cheap). They're fairly easy to identify by the irregular pattern of short, streak-like marks around the barrel. It might be harder to spot if it's recently been reblued, but you can usually look just inside the muzzle. Damascus barrels are weaker than modern barrels and are not designed for the high gas pressures created by modern ammunition.

A Damascus barrel in good condition can be used if you shoot light loads, but if it's weakened or you put heavy loads in it the barrel may burst slightly ahead of the chamber, which could injure the shooter.

I recently obtained a model 215 Riverside (I think it's a 16 G but it doesn't say anywhere on the gun what it is) and it has a Damascus barrel. Luckily, I found a place to order parts and will be purchasing a new one.

Well, it's AT LEAST 50 years old if it's been hanging in a barn, but it's ONLY 50 years old if it's been cared for. If it looks good and the action is tight it is PROBABLY OK, but let an experienced gunsmith look it over and follow his advice.

I am the owner of a Riverside Arms 16 ga. circa 1913 that i bought at a gun auction for $50 and it has routinely out-performed my buddies new TC Contender 12 ga. which we use for grouse.

I own a 16 Ga. double barrel and it out performs most of my newer 12 ga.shotguns, if kept in good working order a gun can last a lifetime,my 16 double was made around 1913 and has the pat.pending date of feb 10 1914 engraved on the base above the triggers. they are fine shooting weapons,but do to their age I'd have it checkedout before firing it.