A couple things to add to Writ's post:
1. You can add media=1 to the [tweet] tag to make the tweet show any images/gifs/etc attached to the tweet. So you'd do something like [tweet media=1]url[/tweet]
2. For some reason, tweets won't show up when you click "Preview" to preview a post you are writing. I'm not sure why. I'm trying to fix that for the next update, whenever that will be.
While you're at it, how possible would it be to add the ability to embed Instagram posts (i.e.
Instagram BBC: Invalid instagram link provided)? Not a high-priority feature obviously, but it would be cool to have.
(And now I'm curious if you have a computer science background)