How cluster a twitter data-set?
k-means is very sensitive to noise

because it is designed as a least-squares approach. Noise deviations, when squared, become even larger.

Twitter is mostly noise

Twitter is full of spam and nonsense tweets. These will be entirely unlike any other and thus have the largest deviations.

Chances are you get one "cluster" that contains almost everything, and the other k-1 clusters consist of a few tweets with their duplicates. Clusters are not topics. They are more likely to be duplicates than topics.

An appropriate clustering algorithm for tweets should probably discard 90% of tweets and produce thousands of clusters. But it will rarely be better than finding all tweets in common - most tweets only have 2-3 usable words.