Probably the best writing tip that anyone has given me is that the last sentence of any given paragraph I write should often be the topic sentence of the next paragraph. Once this was pointed out to me, I noticed it in almost all of my writing and often in student writing as well. This error probably happens because it’s natural to build up a paragraph until it connects to the next point to be made. But how we write is not how we read. Often I can go through a first draft and move the last sentence of many paragraphs to the beginning of the next.
Bonus tip: When a colleague read a draft of my book manuscript, he said that I should try to shorten break up the paragraphs, because the paragraphs would appear longer on the printed page. Sure enough, when the proofs arrived, he was right.