The variable power in the Sheridan will make things screwy if your not paying attention, I agree. Pump too fast or too often and or let the gun sit long after being pumped and accuracy will change. However I have lit a blue tip match with mine using peep sights at ten meters! So the potential is there.
One other interesting thing at least for me. If I hunt and total the game I shoot starting today for the rest of my life I will not put a dent in what I have killed as a kid with that sheridan rifle. I would guess I have killed many hundreds of rabbits, muskrats, norway rats, pigeons, quail, pheasants, ducks, crows at least several fox, raccoons, woodchucks and the list could go on and on. There are so many things I would not even post about that I did with that gun as a youth. I attribute 99% of my current skills as a marksman to that rifle alone. When your 4 and a half foot tall at 12 years old and it takes 10 very hard pumps to make one shot, your learning real quick to make each one count!
I doubt there is a better gun in the whole world for youth marksmanship then the old Sheridan or benjamin rifles!