I have a 76 and both my left side and inside mirror are the same way. From what I understand we are about 65 dollars screwed as there are no adjustments. I was thinking about getting them where I like them and pouring some silicon or something in ball joint, just to hold it in place until I can afford some new ones.
I have not personaly done it but here is what I have been told. There is a tension strip inside the head of the mirror that provides tension on the ball fitting. This strip is held in place by a rivit type fitting. You need to get inside and use a punch on the rivit to tighten everything up. But how do you get inside? Was told that they mirror is held in place by an adheasive. So soak the mirror in a solvent that will break down the adheasive. Read where one guy soaked the mirror in gas for two days and the mirror can out. If you do this do it outside away from everything else just in case. Then tighten up the fitting and glue the mirror back in.
Disclaimer: Like I said, I have not done this, just read about it.
I don't believe my mirrors are stock. They look nothing like pictures of other Stingray mirrors I have seen. I guess they are more "California" style mirrors like the ones found on an 80's Firebird (I guess). They are totally worthless though. All I can see is wheel well. I was going to have them replaced with stock mirrors. Maybe that is why the previous owner changed them in the first place. I guess I better re-think that one.
I have the sport mirrors on my car and they shake too. I was afraid to try to take them apart so I just wedged a small piece of black rubber between the housing and the bottom of the mirror. That fixed the shake. Mine show the road behind you ok but the mirror is kind of small due to its design.