The "avoid trivial edits" guidance is designed to keep otherwise well-meaning user from annoying everyone with endless, overly-pedantic changes that bump every post with trivial "activity." It's a bit user-hostile to have someone micro-editing every post; so we ask that most punctuation and semantic changes be accompanied by substantive changes that actually improve the post.
Having said that, some content is more visible (an thus more important) than others, and needs to be kept in optimal condition. So in order of importance:
#1, Titles should be top notch. Period. There is no excuse for sloppy or vague titles with punctuation or spelling errors. The titles on your front page say a lot about your community, and when experts are drawn to your site, those titles set the authority and tone of your site. It defines who you are. Keep titles pristine, clear, and easily understood.
Edit titles anytime they can be improved or clarified.
Question introductions need extra attention, too. A close second to titles, the opening lines of every question should clearly summarize what the question is about. Don't ramble; Get to the point. Editors: keep them error free.
It's those first few lines that appear below the title on the 'questions' page. Remember that the lifeblood of this site is search; and its the question openings which will drive Google searchers (potential users) to click through to your site… or not. Keep openings clear and error free. Edit away!
Question bodies should be relevant, but concise. This is where editing out unnecessary salutations, ranting, and off topic minutiae is helpful. Edits to improve formatting are often helpful; not all users are familiar with our markup.
Widely-appealing top answers should also be pristine. The top answers in highly-upvoted post get a lot of eyeballs. Make sure everything "above the fold" (i.e. the top-voted answers) get top attention, too. These posts get Tweeted out and reused (with attribution linked back here), and they may even get syndicated by some of our partners. So let's be sure to give that content a lot of love, too.
So what kind of routine edits are appropriate?
Certainly any overly distracting or egregious grammatical errors — especially those that make the post difficult to understand — should be fixed. Always try to edit any comments that help the post back into the body of the text (i.e. don't leave useful information in comments). Beyond that, we like any edits that clearly improve the post. We just don't want to create an overly user-hostile environment where the punctuation-and-grammar police are always ready to pounce and call you out on every little faux pas.