When we style text using italics (either by using the 'i' button, or by inserting <i> or <em> tags in the code view) the tags are removed as soon as we switch views or save.

This is a bit time sensitive so I hope you get this before the weekend (I am in the west coast US so it's late over there!) because we have a bunch of users doing edits

I am sure this must be a setting issue somewhere, but I've been through a backup and the live site and can't find any substantive differences.

We just switched from using 2.50 beta to 2.50 RC6 (not sure if that has anything to do with the situation)
It seems that module parameters haven't been configured properly. Please make sure that you are using a valid twitter username, and that you have inserted the correct keys. Detailed instructions are written in the module settings page.
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