Redundancy - is it a big problem?
Assuming you want to learn sentiment this is a problem. What happens when you feed this to a Machine Learning algorithm is that it will give more weight to the tweets that are in there multiple times, while not learning more information. It's unlikely that a tweet that has been retweeted 10 times carries more significant information about sentiment than one that hasn't been retweeted. What you could do is add the number of times the tweet was in the set as a feature to your sentiment model, it's possible something can be learned from that fact (maybe positive tweets are retweeted more often), but you should keep it at 1 row for every distinct tweet.

Getting rid of these redundant records should not be difficult programmatically though. I don't know what language you are using but if you only consider the body of the tweet (the content) you could iterate over your tweets, keep a list of all the unique bodies, combined with other meta information (like user, labeled sentiment) and if the content of the next tweet is already in there, just do not add it. Look for 'distinct' functionality as opposed to redundant, enough information out there.