*Post Update: Yikes! I misunderstood the problem. Apparently (and I cringe as I attempt to grasp this) the issue is that you can no longer see conversations between people you do follow and those you don’t, but only if they begin their tweet with an @. So if you were Twittering about Tina Fey, and I don’t follow her, I wouldn’t see:
@TinaFey Let’s go for cheeseburgers.
But I would see:
Say @TinaFey, let’s go for cheeseburgers!
Is that right? Please don’t hit me.
Sooo… couldn’t we just work around this for the time being by putting a character in front of the @ sign before we talk to someone? Like so: “FU @Maggie, you can’t begin to grasp my fury.” Et voila?
My tutorial on running search terms is still below. Forgive my misguided first attempt to help, and supply your own ideas in comments. Also, you can tell me if I’m wrong again, and we’ll do this over. The less vitriol the better. Thank you.
As you may know, Twitter recently made a change to how @ replies are received. People are kind of freaking out. If you use Twitter and you still want to see @ replies from folks you don’t follow, do this:
1. Find the search box in the sidebar and type in @ plus your username. I typed in @Maggie:

2. Click on the little magnifying glass to the right of the search box.
3. Verify that your main bar now shows search results on the @replies for that user name:

4. On the top right of the main bar, you’ll see a little green button next to the words “Save this search.” Click there. Here’s a detail view:

5. Look in the right sidebar again. Under the search box, you should see a subtitle “Saved Searches” and a clickable link to searches on the user name you’ve selected. Click on the user name you’ve saved whenever you want to see @replies from everyone, even folks you don’t follow.

For now, I hope that helps. I know it doesn’t address every issue, but it’s an easy workaround for now.