I used to babysit a boy with autism who had similar issues - struggled to unlock a door, wash his hair, close a box, put on a DVD etc. He didn't really use much verbal communication, so teaching him new things was sometimes hard. He was 9 - 10 years old when I worked with him.
Two things that I noticed were particularly hard for him:
- He didn't know how much pressure / force to apply. So if he wanted to unlock a door, he would touch the key and then the door handle, because he knew that was the correct order. But he wouldn't grasp the key and turn it.
- He found it hard to learn by imitation. So even if I demonstrated something multiple times really clearly, he wasn't able to learn to do it himself.
I ended up teaching him a couple of things using a hand-over-hand technique. For example, he had a jack-in-the-box toy that you had to press down hard to close the box. He would try again and again pushing the lid shut, but not hard enough to close it. I showed him how to press harder until it clicked, but he still couldn't do it. But when I closed it with him by pressing his hands down until he felt the box click shut, he could do it by himself after 1 demonstration. I think he needed to physically feel the feedback from the box to understand what to do.
Could you try something similar with your son? Cupping one of his hands around a (just) closed jar, placing his other hand on top and curling the fingers round the lid, then helping him to make the twisting motion to undo the lid? Sometimes you need a bit more feedback about what it's actually supposed to feel like to pick up on a skill. He might be trying to press the jar too much, or squeezing the lid rather than twisting, or twisting the wrong wrist, or not gripping the lid tightly enough, or just not able to co-ordinate all the different actions together.
I don't think hand-over-hand teaching is generally recommended, but in this specific case, where there's a skill he really wants to have (opening a jar) and he hasn't been able to learn by observation or demonstration, it might help him to have it demonstrated using his own hands from his own perspective?