Doing something correctly, i.e. learning the correct way to accomplish something is important. It does take patience on your part to allow the mistakes to happen and then choosing your reaction to the situation.
Make sure that you are allowing him the space to make the mistake and then not jumping on him after it occurs. Appreciating the effort is important, even if you are correcting the behavior. If he is completing a positive activity in a positive way he needs to be recognized for his effort. After that, you can correct the behavior. It is a subtle difference and something you have to be hyper aware of until it becomes natural response.
Your son uses the wrong fingering while playing the piano.
Instead of jumping of the fingering, make a positive comment to start the conversation,
"I see you are working hard"
Then sit and watch for a minute, don't correct the behavior; instead ask,
"I forget, how did the teacher show you to place your fingers. Could you teach me? That looks like you got it, however didn't she say place your pinky a little to the left?"
Empower your son to learn himself and that the process of learning is power in itself. If he needs to learn how to place his fingers on the keyboard. Take a digital photo of the teacher's fingers in the proper position and place it on the piano or allow him to take the photos and work with him on creating a picture book. Don't jump on him to use it, allow the teacher to show him and give him the visual re-enforcement.
Again, if he attempts something in front of others and gets a reaction that he doesn't like, focus on how he felt about it, not on their reaction. Keep redirecting him to how he felt about it, what he did well. Once you have established this behavior/response, then ask what areas didn't he like, or where he wants to improve.
In regards XXXXX XXXXX sheet music, I wouldn't make it a choir, rather a game. Print out different notes and hide them around the house. Print out a scale and place it on the fridge and have an egg hunt style game. Make the process of learning as fun as possible. If he isn't interested in the game at first, encourage with a reward for finding and getting them correct. Remember to set him up for success. If he isn't good at all at reading music, have a copy of a filled out scale on top of the blank one, so he can use it.
The other thing I would encourage is social interaction. Make sure that he has a chance to interact with his peers in low structured activities. Successful social interactions are a huge confidence builder.
I realize that I have focused on the piano lessons as the example, however the same underlying principles apply across the board. The teacher wants him not to worry about spelling because he/she wants your son to enjoy the process of writing (and get out his ideas), once he enjoys the process correcting things is not a threat, it makes something he enjoys better.