On the East Coast, Twitter still down for me on mobile. All the Twitter media resources (twimg.com) are also not appearing.
Twitter is still not loading for me, but just checked Hootsuite and it is up and running now. Hootsuite was down for a while also.
I doubt that your offline playlists were affected ...
Not sure why they were, but I tried 6 different offline playlists and each of them said "can't play the current song", then cited internet detection... which hadn't been an issue.
Now (10:04a) all of my playlists are working again.
Spotify has a terrible network connection algorithm that will sit there and spin forever trying to open the app if it thinks you're on the network but you're really not.
Put your phone in airplane mode, then re-open Spotify, and magically, all of your offline playlists will play.
Twitter was working from my mobile about 15 min ago, but not on my desktop. Now both are down. Can't believe Twitter is down. On my mobile I'm getting notifications, but can't view them. The people who are sending updates are mostly on the East Coast and Canada, so maybe it's back up for them.