Use the [Enter] key to launch the search operation.

That's not even needed using the mobile site on Firefox on Linux, the search results are already listed on the fly...

Could you clarify the steps a little more.
If I search this happens to me:

Here is the sequence as seen on the Kindle, Paperwhite, firmware 5.8.7.0.1
The Kindle is where this needs to work properly, use of the older FireFox on OS X just seemed a convenient illustration of the issue.

Thanks @TenebrisCaelo the screenshots highlight the issue really well. I'm not sure we have a Kindle but I noticed you said "the older FireFox on OS X" -Which version of Firefox were you using?
Could you share the URL of screenshot 3? It might give a significant clue.

Yes I see the same problem if I open the mobile site in an "older" Firefox. It identifies itself as "Mozilla/5.0 (Macintosh; U; Intel Mac OS X 10.4; en-US; rv:1.9.2.28) Gecko/20120306 Firefox/3.6.28"

The URL shown by the Kindle when the 3rd screen appears is "https://en.m.wikipedia.org/wiki/Special:Search"

In case anyone is curious, if I key-in a search on that 3rd screen, no results appear after pressing [Enter] to launch the search. That same empty-search page reappears.

I can indeed replicate the same problem on Firefox 3 hah. It seems that the search submit button is wrapped in a link so the search doesn't submit on certain browsers.

Thanks for the help debugging I think we can fix this easily!

Change 349261 had a related patch set uploaded (by Jdlrobson):
[mediawiki/extensions/MobileFrontend@master] Search button should not be wrapped in a link

https://gerrit.wikimedia.org/r/349261

@ABorbaWMF could you verify this task doesn't break UI on tablets? I tested it on Chrome simulator and Samsung Note 10.1 and it looks great. The Search functionality is an important feature and we should be 100% sure it works on most common devices.

Change 349261 merged by jenkins-bot:
[mediawiki/extensions/MobileFrontend@master] Search button should not be wrapped in a link

https://gerrit.wikimedia.org/r/349261

Tested on en.wikipedia.beta.wmflabs.org/wiki/Main_Page

I was able to perform searches using older versions of Firefox, but I do not have a kindle. The issue appears to be fixed from my perspective.

Systems -
Windows XP2 - Firefox 3.0.11
Windows XP2 - Firefox 3.6
Mac OS 10.7 - Firefox 3.5
Mac OS 10.7 - Firefox 4.0

I also tested some newer browsers to make sure nothing broke. Things appear to be working.