Well now I’m having problems replicating it. I had stopped using the plugin because, in preview, that message would appear. But I just went through a post that had already been published and editing in the plugin, and everything is working. Sorry to waste your time!
I’ve updated to 0.5.0.1. I’ve defaulted to using the version of Blackbird Pie on Twitter Media for the last few posts, but here is an example of a post in which I used the plugin: http://midwasted.com/2011/04/while-you-were-tweeping-4611/
It’s working in those old posts, but new posts only display the “Problem connecting to Twitter.” message. I’ve even tried deleting the plugin and installing via FTP, but it hasn’t helped.
Not sure if this is important, but when I use WordPress’s built in Tweet display (just paste the URL on a line by itself) I get the same error as when I use the plugin.