First of all this is all still in very early beta work ! I'm not sure how it got to HN but here it is so all your feedback is great. I'll try to answer some of your questions the best I can:
1) The top words are those that characterize the show the best. This is not perfect science, and is an output of the LDA algorithm, but it gives already a good indication. Some words indeed shouldn't be there. Some possible explanation: subtitle mistake or a bug...
2) The words that appear more then once are again a glitch, and should be fixed. Again, work in progress...
3) The top topics are found using a topic modelling algorithm. It splits a corpus of documents into a number of topics, and every documents contains a certain proportion of each topic (20% Police, 80% Terrorism for example). The topics are bag-of-words, and so we manually give them names to what we think fits best.
4) Again beta...
I hope the 'about' is clear enough, if you have any questions feel free to ask !