issues with comments to blogger.com posts via mobile devices

Thanks for sharing your problem today - and welcome to the Blogger Support forums.

Your readers need to be identified, using their Blogger / Google accounts.  Unfortunately, some readers security settings block their identity, inadvertently, from the commenting script.  Anonymous comments use the same code sequence - and may also be subject to this problem.

http://blogging.nitecruzr.net/2015/05/when-you-comment-you-need-to-be.html

To comment anonymously, your readers should be solving a CAPTCHA, that identifies them as a person (not a script).  If your readers are able to comment using Google accounts, but not anonymously, they have a script filter blocking the CAPTCHA.

http://blogging.nitecruzr.net/2011/09/blog-readers-report-comments-supposedly.html

First, as individually possible, each reader should clear cache, cookies, and sessions (yes, all 3) - then restart the browser, and check again.

http://blogging.nitecruzr.net/2010/11/clearing-cache-cookies-and.html

Your readers problem start with a filter, on their computers.  The Blogger / Google login status, and the ability to post comments, is sensitive to both cookie and script filters.  Your readers may need to enable (stop filtering) "third party cookies", in their browser and on their computer. And, have them check their script filters, too.

http://blogging.nitecruzr.net/2016/04/blogger-magic-enabling-cookies-in-your.html

http://blogging.nitecruzr.net/2016/04/blogger-magic-enabling-scripts-in-your.html

Third party cookies filtering, in a browser setting, is the most common solution, overall - but your readers may have to search for other filter(s) that affect their use of Blogger / Google.

http://blogging.nitecruzr.net/2010/11/blogger-layered-security-and-you.html

If any security product has a "block" list, ensure that "blogspot.com" is not in the "block" list.

Any filters are subject to update, by the creator.  If the problem started a few days ago, your readers may have to look on their computers, and find out what product or accessory was updated, a few days ago.

http://blogging.nitecruzr.net/2014/01/almost-nobody-controls-their-own.html

[FAQ] Why Can't I Access My Blog / Comment / Follow Blogs?

Trying a different browser or computer is a good diagnostic technique - though not always a permanent solution.

http://blogging.nitecruzr.net/2013/09/diagnose-problems-using-differential.html

I hope that this helps you understand your problem!  Please, let me know if you have more questions!