Recently making a SP2010 site responsive for a client and came up to this issue. The drop downs don’t show at all and the mark up is all over the place. I found this fix from the web and it’s helped out massively.
The issue is that the browser user agent sniffing done by ASP.NET looks for the string “60” in the AppleWebKit version portion of the User Agent when attempting to sniff out a (now) ancient version of Safari, and the new version of Safari on Mac OS X or iOS 8 looks like this: AppleWebKit/600.1.17 (this is the desktop Safari version for this example – iOS is similar)
See a problem? It found the 60. Right there in the beginning of the 600.
Because it doesn’t feel comfortable with that version of Safari (remember, it thinks this brand new version is actually a really old version), a setting regarding the control adapter (a sort of ASP.NET plug-in, if you’ll excuse the poetic license) that handles the
Asp:Menu for SharePoint’s navigation isn’t applied properly.
In your web site’s inetpub document root (check IIS manager to see which folder belongs to your SharePoint site), find the App_Browsers folder, and just drop in this file. Due to another ASP.NET bug, you’ll also need to “touch” an existing file in that folder – so just open the
compat.browser file already there, make an edit (like adding a space to the end) and save it. Once that’s done, reloading your browser on the affected devices should show the working fix.