May 10 was the day termed "Patch Tuesday" - the day when Microsoft releases important security related patches, to its various Internet updated products. During the 3 weeks after May 10, we've seen a significant number of security related discussions, in Blogger Help Forum: Get Help with an Issue.
It appears that Microsoft updates, for May 2016, affect use of Blogger.
The Microsoft Security updates, applied May 2016, appear to have affected various Blogger features, that are known to be vulnerable to layered security.
- CAPTCHA visibility when daily post limit is exceeded.
- Publishing comments, or replying to published comments.
- Quick Edit icons.
- Followers / Reading List maintenance.
- Stats self initiated pageviews.
All of these features are known to be affected by cookie filters, and / or by script filters.
If you are using a computer that runs either Microsoft Windows 7 or Windows 10, and you are experiencing a problem with publishing comments, or with using Quick Edit, or with blocking your own views in Stats, or similar problems, you may want to check your cookie and script filters.
I note that some of the reports mention the browser used as Chrome or Firefox. You'll want to check filter settings in Windows Security Essentials.
Being realistic, it's also possible that Microsoft broke something within Windows - but we'll have to wait patiently, for them to admit that.
If you need different or more advice, please start a new topic in Blogger Help Forum: Get Help with an Issue.
Microsoft released monthly security updates May 10, 2016 - and since that date, there have been a number of security filter related issues, reported in Blogger Help Forum. It appears that the the Microsoft Updates involve cookie or script filters, which affect use of Blogger.