I see only 2 options. What browser are you using?

Firefox 31.0 and Google Chrome 36.0.1985.143.

It is caused by enabling the beta feature "New search" on
https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-betafeatures
(the problem also disappears if I access the page logged out).

Aha, that's what paraminfo returns: https://en.wikipedia.org/wiki/Special:ApiSandbox#action=paraminfo&format=json&querymodules=search

So it's a CirrusSearch problem.

Looks like we just need to get rid of any 'CirrusSearch' entry(ies?) from $wgSearchTypeAlternatives when the BetaFeature is enabled in CirrusSearch\Hooks::initializeForUser.

I can have a look at it in a day or two. If anyone is closer to having the right plugins setup and wants to do it please let me know.

Change 156691 had a related patch set uploaded by Manybubbles:
Clean up options with betafeature

https://gerrit.wikimedia.org/r/156691

A day or two turned into two weeks but who is counting now that there is a patch.

Change 156691 merged by jenkins-bot:
Clean up options with betafeature

https://gerrit.wikimedia.org/r/156691

Should be fixed now.