user8486: There are two cases that bother me:

A user made a very minor edit to a post, like capitalizing the i's or fixing one or two spelling or grammatical errors that don't impede reading nor understanding.
An anonymous user added more information to a question or answer. There's a chance that the edit was made by the post owner who didn't bother to log in, but it could also be someone else who might or might not have a clue about the content of the post they were editing (especially with identification-request questions, the added information might not even be about the same series as the one requested).

Should I accept or reject those suggestions, and on what grounds (which reason for rejection should I select)?

user1398: 
A user made a very minor edit to a post like capitalizing the i's or fixing one or two spelling or grammatical errors that don't impede reading nor understanding.

If it fixes error and does not introduce more error (or one or two errors that can easily be fixed by editing):

If you find that the post has other thing to be improved, edit it the post to fix the rest of the problems and mark the suggested edit as helpful.
If you find that the post has nothing else to improve, just approve the edit.

Although I suggest editing the post to fix the rest of the errors, if it is over your capability, don't do it.

An anonymous user edited a question or answer, adding more information. There's a chance that the owner of the question or answer posted anonymously (because they didn't log in), but that edit could also be from someone else, who might or might not have a clue about the post owner's intent (especially with id request questions, the added descriptions might not even be from the same as the one requested).

For question's case, it depends. Since many users are not properly registered, the cookies are lost and they can no longer access the account they used for asking the question. We might give some leeway for identification-request questions, since they are effectively abandoned for the case of unregistered users. In any case, check that the edit actually improve the question in a sensible way. If it does not, just reject it.
For answer's case, the bar must be raised higher: we must make sure that the edit is relevant to the question being asked, and it is of high quality. Just reject anything subpar.

8486: <p>There are two cases that bother me:</p>

<ol>
<li>A user made a very minor edit to a post, like capitalizing the i's or fixing one or two spelling or grammatical errors that don't impede reading nor understanding.</li>
<li>An anonymous user added more information to a question or answer. There's a chance that the edit was made by the post owner who didn't bother to log in, but it could also be someone else who might or might not have a clue about the content of the post they were editing (especially with <a href="https://anime.stackexchange.com/questions/tagged/identification-request" class="post-tag" title="show questions tagged &#39;identification-request&#39;" rel="tag">identification-request</a> questions, the added information might not even be about the same series as the one requested).</li>
</ol>

<p>Should I accept or reject those suggestions, and on what grounds (which reason for rejection should I select)?</p>
 1398: <blockquote>
  <p>A user made a very minor edit to a post like capitalizing the i's or fixing one or two spelling or grammatical errors that don't impede reading nor understanding.</p>
</blockquote>

<p>If it fixes error and does not introduce more error (or one or two errors that can easily be fixed by editing):</p>

<ul>
<li>If you find that the post has other thing to be improved, edit it the post to fix the rest of the problems and mark the suggested edit as helpful.</li>
<li>If you find that the post has nothing else to improve, just approve the edit.</li>
</ul>

<p>Although I suggest editing the post to fix the rest of the errors, if it is over your capability, don't do it.</p>

<blockquote>
  <p>An anonymous user edited a question or answer, adding more information. There's a chance that the owner of the question or answer posted anonymously (because they didn't log in), but that edit could also be from someone else, who might or might not have a clue about the post owner's intent (especially with id request questions, the added descriptions might not even be from the same as the one requested).</p>
</blockquote>

<p>For question's case, it depends. Since many users are not properly registered, the cookies are lost and they can no longer access the account they used for asking the question. We might give some leeway for <a href="https://anime.stackexchange.com/questions/tagged/identification-request" class="post-tag" title="show questions tagged &#39;identification-request&#39;" rel="tag">identification-request</a> questions, since they are effectively abandoned for the case of unregistered users. In any case, check that the edit actually improve the question in a sensible way. If it does not, just reject it.</p>

<p>For answer's case, the bar must be raised higher: we must make sure that the edit is relevant to the question being asked, and it is of high quality. Just reject anything subpar.</p>
