I had missed this question, so until recently I was unaware that questions from Meta were going out on Twitter.
A suggestion: rather than excluding support and bug, can we consider this from the other direction, of what questions might be of most interest to people who don't know about Stack Exchange already?
If we Tweeted the Meta questions tagged featured it would allow us to send out the Qs about the Weekly Topic Challenge and the Weekly Chats, but not the everyday Qs about the internal workings of the site, which have less interest to the non-SE audience.
Another option might be to create a tag for Meta called [tag: tweet-me] which would indicate that the Meta question is Tweet-worthy. This might allow the sites to control their own Twitter content with less processing load on the system; surely it is easier to check for the presence of a tag than it would be to calculate a question's worthiness by some other algorithm.
The reason I ask this is that new users who look at @StackGenealogy in order to consider whether they should follow it may not be familiar with Stack Exchange's way of doing things. If they see a list of questions about our content, they may be tempted to come and answer some of the questions.
Once they are here, we can indroduce them to the joys of Meta, but I don't think Meta discussions are particularly useful as an advertising mechanism.
I have posted an answer on the Meta question mentioned by @PolyGeo in the contents: Should site-specific Twitter feeds be tweeting meta questions?