First, you could consider creating a pseudo account and then follow the person, that way you will be seeing all their tweets.
You could find out if they use a link shortener; twitter link shorteners makes the account lose some protection, thus if you find the link you can access the tweets.
If you have a friend who is following the said person you could borrow their logins and view the tweets using another person’s account, that way you needn’t bother following them.
You could also consider searching tweets replies to the original posts, that way you could get an idea of what the tweet is all about.
Lastly you could find out the internet address of the persons profile, access the address and read the tweets. Such an address will normally look like “http://twitter.com/#!@%/”