A new day, a new feature in Twitter. And this apparently has just been implemented. It is the ability to see the profiles you access which users you and the person whose profile you are viewing below.
In the column are only shown 6 clickable avatars, but a link below the list shows which are all followers in common. There was no official announcement of the new feature yet. It is also unclear whether the feature is available through an API so that developers include the common followers to its customers.
Meanwhile, the ability to disable the official retweet still missing.
update | Apparently this feature is being released gradually to service users. Specifically 10% of them, according to what I could ascertain the actual network. Strangely, I had this enabled field but now I do not see more. Twitter is no longer with my face.