It would be a neat feature for the Community bot to automatically detect when the last users posted question StackOverflow question is identical to their last posted question on any other Stack Exchange site.
User posts a poor question on StackOverflow and it receives no attention after a few hours
User gets impatient and posts the exact same question on Programmers hoping to bring attention to a different audience.
As a Programmers mod, we have become accustomed to the duplicate SO question check as a manual process, because this happens all the time. We spot this and close the question as off topic.
It may seem like an expensive check to perform when a question is posted but not if the question body is computed and stored as a hash in a seperate field. Comparing identical hashes would be much cheaper so it is certainly a feasible feature.
I also see the benefit for other Stack Exchange sites as well. I post a question on Mathematics and it is not answered, so I immediately cross post onto Cross Validated hoping to double the chances of getting an answer. Without this feature, many of these occurrences may never get caught.
When this situation is caught a simple Community Flag brings it to the moderator attention where we can handle it from there.
A simple version of the same process is one where somebody links to their existing question from another Stack Exchange site. This can also sometimes be something that a moderator may want to look at.