I do quite a bit of weights for a sport I practice pretty intensely. Part of our testing involves as many reps as you can do in two minutes in various exercises one of which is chins. Essentially any leg movement can help you quite a bit, we call it a swing, and as an example without a swing some of us can do somewhere around 40-50 chins in the two minutes, with a swing you can get over 100.
It's all about rhythm and, sadly, not about using your muscles properly. If someone is perfectly healthy and in no risk of injuring themselves (wouldn't that be nice) i would say do chins with as little body movement as possible to get the maximum benefit. if you lever your legs up and hold them there the entire time that is great, it become as ab exercise as well. But there should be no leg movement if possible. I tend to have my knees bent and ankles crossed over, but i try my best not to move them at all.
As for the wide vs. close, i too find the wide slightly easier and i have one bad shoulder. The reason i like the wide grip is because, as you point out, it feels easier on the shoulder. I think it is easier on the shoulder joint, and if you think about it and go wide enough you're not pulling yourself up as far because you've spread out your hands.
Here is a hint for shoulders and loose joints: stop if it hurts. I know it can be hard to do so, but i've hurt myself more than a few times and watched people hurt themselves numerous times. The best way to strengthen your shoulders isn't chins but various rotator cuff exercises. Here is a link to the best video, i could find, of the most effective exercise i've ever used for building shoulder strength: http://www.youtube.com/watch?v=8KUzqNBeqAw&NR=1&feature=fvwp
Remember to use very light weight 1-2lbs at most! and go slowly with your movements. I personally find it more effective when i don't support my upper body with my elbow, as in the video, but when i am lying totally horizontally. There are more exercises but this one is great.