Microblog readers should detect duplicates and suppress displaying them. I have a couple of Twitter accounts, an Identi.ca account, and also my Facebook account: I see many duplicates.
It would be best if the microblogging services would generate unique message IDs on post, and then preserve them on read and syndication, but it's probably too late to demand that they do that, as each service wants to think of itself as "Special" and has little interest in "playing well with others" in a larger media stream ecology.
But even without that, a smart microblog aggrigator/reader should be able to notice things like "I've just seen this exact tweet from this poster, just read from another logged in account", and fold them together. This would be useful for the common case of reading more than one twitter account that has some of their follow list in common.
The metarule is "reduce the cognitive load on the user". Anything that makes it easier for the human in the loop to read and understand the stream faster and easier, is better.