I'm a self taught shooter so I'm trying to find some advice. I have an older used bow that I bought to learn. As far as height, I'm pretty much right on, but usually miss my aim point to the right. Any suggestions?

Move your sights

Sounds sensible!

move them slightly to the right

Where ever your arrow group consistently hits, move your sight to match it. Example...Aiming point bulls eye, hitting low and to the right, adjust your sight down and to the right. This will bring your arrow group to the bulls eye. Also check that you arrow is coming out of the bow straight. To do this, nock an arrow, hold the bow in front of you, line up the bow string with the riser dead center both above the arrow and below the arrow using your dominate eye with the arrow pointing up slightly, once you have your string centered on the riser adjust your arrow rest so that the arrow is inline with the bow string by loosening the rest and moving it left or right. You should notice that your bow sight pins will be fairly close to this center line when you eye it up as well. I hope this helps.

Only change the sights based on multiple shots. Look for a grouping when adjusting the sights.

Also, try to use the same type of arrows.

All good advice already.

I have 3 points that I hit prior to each shot: jaw, nose and fingers of the hand that holds the bow. This creates a set point for possible areas of error and verifies that each shot is made with the same lock points. At 20 yards, I didn't notice much difference but when I moved to 50, it closed the gap tremendously.

If you are right handed, make sure you are following through your shot. Many shooters hit right because of the after shot. Also, torquing the bow is possible. Make sure your grip isn't too tight. Good luck and keep at it

Such great advice so far. For me if I dont square up my shoulders from initially pulling string back I notice my 40yds and out groups arent as consistent as they should and have been. Dropping your bow shoulder at the shot instead of letting the bow fall straight away towards your target is very important.

All good points. One other thing that can help with consistency and follow through is to make sure you are pulling and holding your drawn bow with your back muscles. It should feel like you're trying to touch your shoulder blades together. It is sometimes referred to as back tension and it helps keep everything in a straight line to include your follow through. Whenever my groups start to get sloppy it is one of the first things I check and it usually tightens things up.
As for sight adjustment, the phrase I use is "follow the arrow" in your case following the arrow to the right with your adjustment will bring your point of impact back to the left. Good luck.