We're seeing a variety of problems, reported in Blogger Help Forum: Get Help with an Issue, by blog owners and readers alike.
Long ago, for blogs with readers who were not really comfortable with maintaining security on their computers, we would recommend changing comment form placement.
The full page (or the slightly less preferable popup window) comment form was more usable, with readers who do not know how to properly maintain cookie and script filters. With recent changes in Blogger and Google, all Blogger comment forms are now vulnerable to inappropriate filters.
- Use of the Google "One account" login creates login cookies under "google.com" - not "blogger.com".
- Publishing blogs to custom domains - not "blogspot.com" - makes cookie access "third party".
- Referencing blogs from countries subject to country code aliasing - not as "blogspot.com" - makes cookie access "third party".
- The new, mandatory commenting CAPTCHA form, part of all Blogger comment form placement options, makes cookie access very important.
The Google "One account" login, at "google.com", is now used by many blog owners and readers - instead of the Blogger native login, at "blogger.com". When the "blogger.com" login was used, cookies created under "blogger.com" were not as vulnerable, to cookie filters.
Whether used under "blogspot.com", or whatever country code alias or custom domain is in use (for the embedded comment form) - or under "blogger.com" (for the full page and popup window comment forms) - login cookies created under "google.com" (by the Google "One account" login) are vulnerable to "third party" cookie filters.
Blogs published to custom domains are becoming more and more popular. All blogs published to custom domains, which use the embedded comment form, are vulnerable to "third party" cookie filters.
Blogs referenced under country code aliasing are becoming more normal. All blogs subject to country code alias redirection are vulnerable to "third party" cookie filters.
The new, mandatory commenting CAPTCHA form needs to access the Blogger / Google login cookie - so blog readers, who are logged in to Blogger / Google, will not be subject to the CAPTCHA. The embedded, full page, and popup window forms are equally vulnerable to "third party" cookie filters, given the above discussed issues.
Thanks to the Google "One account" login, as Blogger is made a way of life to more of a reader population who have no interest in maintaining security on their computer, these issues will become more problematic.