One of the fundamentals of testing is isolation - how do you make your test environment as isolated as possible. When you're dealing with internal resources, this is fairly easy as you have complete control over the environment. External resources, not so much.
For this instance, I would recommend you create a couple test twitter accounts. (I would hope it's not against their TOS, I would check this first.) You might have TrarothTest and TrarothTestFollower. You could have it auto post to TrarothTest, and then wait to verify that TrarothTestFollower has acquired a new tweet from TrarothTest.
So you're dealing with accounts you have complete control over, isolating the environment as much as possible.
You will run into things from time to time you can't control with this. What if twitter is down (and what would hipsters do while twitter is down? :-O) or someone drives a shovel through your local fiber line running out of town? In this case, it would seem you need an alternative: a locally hosted twitter site. It might be a lot of extra work to maintain, but you could send the traffic to your local site and make sure it's what you would expect. Then simulate the tweet and "verify it happened".