Looks like Hanley beat me to the punch but I totally concur with what Hanley says above. Concord, feel free to jump in here at any time…

Leone has taken an 1866 Winchester Yellowboy and “cut it down” to look like an 1860 Henry Goldenboy. The Henry is loaded from a slit located towards the muzzle end of the tubular magazine under the barrel. The Winchester is loaded by a slit located on the right side of the receiver which Clint does a pretty good job of hiding during the shooting scenes but is still visible several times while shooting. The Winchester has a “ring” that holds the wooden fore stock or handle to the magazine and barrel. As you can see were the prop masters have removed the wooden fore stock the top half of the ring still remains on Blondie’s weapon and it does indeed look to me as if a scope has been added to the left side of the gun to make it look like the remainder of the ring has a use for securing the scope to the gun. The Winchester also had a ring that attaches the magazine to the barrel at the muzzle of the gun. The Henry has no such ring. Also, the Henry's, as far as I know, had an octagonal barrel not a round one.

The top two guns are '60 Henry's and the bottom gun is a '66 Winchester. I have circled the loading gate on the Winchester which you can clearly see in a few of the scenes below. I also circled the strap the attaches the wooden fore stock to the barrel and the strap that attaches the barrel to the magazine on the Henry.
The loading gate on the "cut down" Winchester.

The "cut down" strap that at one time attached the wooden fore stock to the barrel.

The front stap that attaches the barrel to the magazine on the Winchester. No such strap on the Henry.

A clear shot of "the thing" on the left side of the gun...

Not exactly the same but here is an image of a scope of the time period that looks very similar. Although Blondies scope looks to be copper this one is brass.

Another good shot of "the thing".

Clearly you can see the sunlight reflecting off glass in these two shots which leads me to belive that it is indeed a scope of some sort...

As far as Clint’s shooting is concerned he is ambidextrous. In several movies he shoots a rifle left handed and in others right. In real life he is more prone to use his left. As you can see in some of the scenes if you watch real closely he is not being real careful as to taking the shot, almost shooting from the hip so to speak. In fact a lot of the times he actually closes his eyes right before he pulls the trigger which is a big no no for sharp shooters. Maybe Blondie is just that good with a gun…