These are some of the most popular add-ons that there are for Firefox. Assuming you are using the official mozilla site then they will be safe.

Not sure why that happens, I have seen similar myself; maybe someone will enlighten us ?

I have never seen an extension which was "verified". As I recall, that message was added to Firefox 2.0, back in Oct 2006, maybe even Firefox 1.5 in Nov 2005. I vaguely recall some discussion of that new "feature" taking place in the MozillaZine Builds forum, about it not being complete - the "author verification" parameters needed more work before it was completed.

My best guess is that the person behind that feature is no longer with Mozilla development (lost some good people to Google in '06 & '07, who may have ended up creating Chrome), and no one stepped forward to "take ownership" of that module.

That said, the Addons website has been completely rebuilt at least twice since that days of 1.5 / 2.0, with many minor changes and improvements, too. IMO, feature isn't really as necessary as it was in those days. There is an extensive, multi-stage screening done as part of the upload process; nothing is even allowed on the AMO servers without passing the "screening" process. Then all new extensions get a preliminary code review before they are made "public". Then there is some type of "sandbox" warning for new extensions showing at AMO until they reach a certain number or level of downloads - that I am not familiar with that, I haven't kept up with the changes over that last few years. IMO, they're fixing stuff that was working and confusing their users in the process.

But Addons obtained elsewhere, would benefit from "author verification", so the user needs to be careful with those non-AMO hosted Addons.