I'm using a Dell Streak mini-tablet with Android OS and am unable to tap the zone drop down box but I am able to select and type in the text fields for search. This problem has been persistent for as long as I've been using your site. Up until now though I was only unable to select the zone for the Character page, and was still able to select it on the Guild page. So that way I was still able to look up my character through the guild. However, now with the changes to your site (which look nice!) I cannot select the zone on any pages anymore. Not sure how you can fix that.
Also while signing up to be able to post I noticed your registration form (and change avatar in the options) is not updated to Mists of Pandaria. It wouldn't allow me to put my character level as 90 or select my race as Pandaren. And there is no monk option for class (though I'm not a monk). I had to use an alt that wasn't a Panda.
Love your site; works great from my computer haha, just not my phone.