I've gotten good results from this in tai chi, qi gong (especially a side bend which had been jammed up for something like a year-- once I started paying attention to how I led into it, I realized I was bending bits of myself forward or backward (sorry, don't remember details) in a way which made a good side bend impossible), and clearing up some knee problems when going down stairs. (I've got a better method now, but the attention to preparation would clear them up for a few months.
I believe this is more useful than trying to correct posture because it's working with immediate sensory information (the low-quality preparation you just noticed) rather than a guess about what better posture is. I also hope (but don't have proof) that working with this approach leads to better baseline movement habits. In general, people are best at noticing changes rather than background conditions.
I'm curious about how useful this advice is-- on the one hand, I've put a lot of years and professional help into improving my kinesthesia, and on the other hand, I started out pretty numb. I don't know how many people would think this is too obvious to be useful, and how many would find it impossible to do. If you do try this, I'm quite curious about how it went. Even if nothing happens, I might find a way to improve my explanation.
The hardest thing for me is keeping it honest. It's essential to pay attention to what's happening during preparation each time, and not slop over it because I think I know how things are going to feel and what changes I need to make. The truth is that I'm using this technique because I need to keep getting fresh inputs.
If you're playing with this, I recommend starting with good-sized physical movements. I've tried it with talking. It's harder, but possible. It may be worth noting that the Alexander Technique was invented because F.M. Alexander couldn't directly inhibit his habits around speaking, so he developed a subtle movement which makes for a general improvement in one's kinesthetic sense. It's also possible to use this method with breathing (take a moment to notice whether you're doing anything extra before you inhale and/or exhale), but I've found that the improvements are larger with bigger movements.
The Five Tibetan Rites, a sort of yoga/calisthenic combination which is worth a separate post.
 The Alexander Technique and me is also worth another post.
Addendum: I believe it should be possible to continuously notice and undo inappropriate preparations while in action, but I'm not there yet.