I am interested especially in whether one can get the right to delete the others' comments.
Unfortunately, from what I read there are no more privileges after 25k reputation. Is this right?
From the FAQ What are the reputation requirements for privileges on sites, and how do they differ per site? at Meta Stack Exchange (specifically, see the section titled "Privileges not tied to a specific threshold"):
- For every 1,000 reputation after gaining the moderator-tools privilege, you gain another delete vote. (Delete votes are capped at 30 per day.)
- For every 2,000 reputation, you get one bonus flag per day. (You also gain bonus flags for casting helpful flags.) (Flags are capped at 100 per day for comments and 100 per day for posts.)
While not specifically tied to your overall reputation, a privilege you can unlock by gaining more reputation specifically in a tag is the so-called "dupehammer":
- If you have a gold tag badge for a certain tag, you can bindingly close and reopen questions using that tag as duplicates, and can modify the duplicate links on such questions, within limits that prevent gaming the system.
- Specifically, the privilege works like this: consider all the tags currently on a question. Eliminate those tags that you don't have a gold tag badge for, and eliminate those tags that you were the first one to add in (per the revision history). You can exercise the privilege if and only if there is at least one tag remaining.
For your specific question, the answer is, "No". You do not get the privilege to delete other users' comments no matter how much reputation you earn.
Like all other users who have the ability to flag, you too can only flag comments for deletion. Of course, in certain cases your comment flag can result in immediate deletion of the comment, but that behaviour is not tied to the amount of reputation you have earned. More details about that can be found in the FAQ How does comment voting and flagging work? at Meta Stack Exchange (specifically, see the section titled "Comment flags").
Only diamond moderators have the privilege to delete other users' comments.