Twitter – How to stop unsolicited tweets

To see all tweets, from anyone, directed to a certain user, you can simply search for "@username". For example, try https://twitter.com/search?q=%40codinghorror to see all replies to Jeff Atwood.

I think I originally misunderstood the question, here's my original response:

Yeah, person A's Twitter replies to person B (tweets that begin with B's @username) are only visible in the Twitter stream of those followers of A who also follow B. I think this feature is fairly non-obvious, especially for new users.

To my knowledge, the easiest way to see also the "@ replies" (without following the other user) is to go to the user's profile (at the Twitter website: http://twitter.com/username, or through some Twitter client) and see their full tweet list there. However, then you'll of course see "@ replies" to everyone, not just to the individual you were interested in. To put it otherwise: no, there isn't an easier way. To see full "conversations" in your feed, you'll have to follow both (or all) parties taking part.

Yes, it could either be that particular tweet is not part of a conversation (i.e No one replied to it or the tweet itself isn't a reply) or it maybe part of a conversation but the other person has protected their tweets.

EDIT

Protecting your Tweets

To protect your tweets Log in to Twitter and navigate to your Settings. Then scroll down and tick the check box Protect my tweets

Then click Save to confirm your changes.