While the full on Twitter embedding would be nice, if that’s not possible can we at least have images appear? A lot of people post Tweets solely because of the images, and forcing users to leave the site just to see the image(s) is not very friendly.
Instagram embedding actually has the opposite problem right now. It only embeds the image, and you would never know that the image was actually an embedded Instagram post. It should at least include the caption and the Instagram username.