Twitter is a public venue unless you choose to set your profile to private. When you are private, you have to accept friend requests (or who views your profile, otherwise anyone can read it). When you run into problems with followers or they continue to post offensive material, you can block a member on Twitter. This is done by viewing their profile and clicking "Block/Report." There is no alert sent to the users to warn them of the blocking. However, there are a few ways to check if you have been blocked by a user.
Set up a second free Twitter account with a different user name if you cannot read a person's Tweets. This will happen if they set their profile to private. Request to follow the private profile. If they accept, you will then be able to read their Tweets again on your new profile.
Try adding the person to follow by clicking "Follow" on his profile. If you are blocked a message will appear stating the user blocked you. You will be able to read the person's tweets if they are public, but you will not be able to contact him via Twitter or follow him.
Tweet the person with an @ reply. On the main home page, type @ and his user name on the search box on the right side of the screen. If your Tweet does not appear, this means he did not get it, which is most likely because you have been blocked.