The column suggests specific ways to go back in time with RSS feeds and the Twitter search option, depending on exaclty how and why you use Twitter. Check out the whole article here.
But probably the easiest solution is to not catch up at all. Why?
If Google is the Web's library or reference desk, Twitter (as it's been pointed out to death) is the coffee shop or pub where the pulse of the community can be heard in the moment. Unless you were a cop investigating a crime, it might seem odd if you walked into the pub days later, and interrogated all the patrons about the specific conversations you missed.