I ran into the same problem -- the dreaded "Sorry, can't connect to Twitter" error. For me, the underlying cause seems to have been some broken GConf settings.

My fix was to use developer mode to completely nuke all of the GConf settings for Internet connectivity. Beware: This fix is not for the faint of heart, and even though it worked well for me, I don't guarantee that it won't badly screw something up on your N9.

Using the shell provided by developer mode, I ran

Then I rebooted the N9. You'll need to re-set up your Internet connections. I think this also ends up nuking your power saver settings and your bluetooth settings as collateral damage. But right after doing this procedure, I was able to sign in to Twitter whereas before no matter what I did, Twitter would fail.

Thanks to vitaminj, whose logged comments in #harmattan from a couple months ago showed me the solution. (See in particular the series of messages starting at 22:52.31.)