How can I find all public comments for a Github user?

You can do this with an advanced search query. In the Issues search box, enter "commenter:username".

Or if you want to search a specific repo: "RepositoryName commenter:username".

This link is quite useful, it's a live feed of all issues you've commented.

https://github.com/notifications/subscriptions?reason=comment

Alternatively, this link is also helpful and is probably what the OP asked (issues where one has written comments):

https://github.com/search?l=&q=commenter%3AVadorequest+is%3Aissue&type=issues

Replace "Vadorequest" by the username you're looking for

You can also use the global search with commenter:Vadorequest is:issue to achieve the same result

Also, if you want to track discussions you participated in, this link might help:

https://github.com/search?l=&q=commenter%3AVadorequest&type=discussions

Replace "Vadorequest" by the username you're looking for

You can also use the global search with commenter:Vadorequest to achieve the same result

This 4th (and last) is not related to the OP's question, but might come in handy. It lists all PR you were requested as reviewer.

https://github.com/notifications/subscriptions?reason=review_requested

Type involves:<username> in the search box on the GitHub's main page. This will find all the issues that the specified user commented on, was assigned to or mentioned in.

For example, if the user's name on GitHub is unclebob, the search query should look like:
involves:unclebob
Or when searching information about yourself if you're logged in to GitHub, simply:
involves:@me

Note, that unlike involves similar search qualifiers - author and commenter - will omit certain results from the search:

• author will find only the issues that were started by the user; if the specified user comments on the issue that was started by someone else, author query won't return it in the search results.
  E.g., compare involves:unclebob and author:unclebob type:issue.

• commenter will find only those issues where the specified user commented second or later (creator of the first comment in an issue is considered its author and not a commenter); if the user starts an issue and then never comments on it, the commenter query won't return it in the search results.
  E.g., compare involves:unclebob and commenter:unclebob.

In other words, when it comes to searching comments, author and commenter return only a subset of involves' results. So I recommend using involves not to miss anything.

Since GitHub Universe 2016, the profile page has changed.

It still has a "Contribution activity" though, which includes your own comments. But you might need to click on "Show more activity" to see past the last few weeks.

And you can email yourself your own activity since last June: "Email updates about your own activity".