My first experiences with Stack Exchange were on WordPress Development. Early on, I tried fixing the grammar on a few posts and got my suggested edits rejected. The reason given was that the edits were too minor and not substantial. So I quit doing it.
However, on a few sites now (including this one), I am a 2k user with the edit privilege, which means that my edits happen immediately with no approval needed. I now edit grammar problems on those sites as I see them, and no one has ever complained to me yet.
This brings up one of the problems with making minor grammar changes: If you are a low-rep user, your edit has spent not only your time, but the time of at least two high-rep users to review your edit. I can now understand the policy at WordPress Development: Posts over there often have poor grammar (but are intelligible), and they don't want to clog up the review queues with edits that are not necessary. So they discourage low-rep users from making those edits by rejecting them. High-rep users are free to make those changes, because the only time they are wasting is their own.
A second (lesser) problem occurs when you fix one grammar mistake and leave a whole bunch of others. Other edits are then needed to fix the other problems, and then the question's revision history gets lots of entries in it. This used to be a problem because once a question got edited several times, it was automatically converted to Community Wiki. SE has since removed that
bug feature, so this is less of a problem than it used to be. Still, if a question gets edited lots of times, it keeps popping up at the top of the front page, which might annoy some people.
A third problem happens if someone says to himself: "I've got nothing better to do this afternoon, so I'm going to spend the next four hours going through old questions and fixing grammar." What happens then is that all of these old questions fill up the front page. The new questions that people want to read then get pushed off the front page, and get less exposure than they would normally get. This makes it harder for people to find the important activity on the site. Use caution and courtesy when editing old posts.
A final problem that can happen is this: sometimes people change punctuation or reword sentences in an attempt to fix the grammar, but they change the meaning or make the grammar worse instead of better. If you are going to make edits, make sure they are correct.
Fixing grammar on posts is good for the site, in my opinion. However, be aware of unintended consequences of your actions. Try not to waste others' time or annoy other users. And if you are going to edit a post, review the whole post; don't fix one problem and leave others. Finally, when you make a grammar change, make sure you are right.