Does anybody know how one can improve in this respect?
My best advice, though it might not be helpful to you, is to have someone else proofread it.
Possible, but that reflects on my performance if they do indeed find mistakes I could have corrected. The goal is to eliminate most of the stuff myself so I don't waste my co-workers time.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.