I don't personally think there is a good way to handle this. The best compromise is that this type of infinite scrolling only comes along with a fleshed out, well working and prominent search and filter feature.
In the case of Twitter, ctrl-f would allow me to search through my bookmarks, my feed or the replies of the tweet I am looking at. Can the Twitter search do these things? If it can, it's really not obvious, and if not, that sucks because a lot of usability is going out the window with no replacement.