If I just say "I must be a difficult man to find a flatmate" without "for" at the end of the sentence, does it become a wrong sentence?
Yes, the sentence does become incorrect. The sentence sounds really weird without it. The word "for" is used here to indicate that Sherlock (the subject) is a difficult person to live with and has a difficult time finding a flatmate. Here are example sentences with "for" used at the end of the sentences. Ex: He is a difficult man to work for. Ex: Who do you work for? Ex: What are you doing this for? Ex: I am an easy person to buy Christmas gifts for.