1. Limit the universe of discourse to very specific facts for which randomness can easily be generated. For example, generate 25 statements of the sort "I just picked the top card off of a deck of cards, and it was X." [Very narrow. Also, one person's random facts would be indistinguishable from another's.]
2. Generate random English sentences using some sort of Markov model. Filter out all those that are false or not about you. [Be prepared to wait a while.]
3. Write a rather large list of true facts, then select a random subset. [Still suffers from interestingness bias.]
4. Produce only like/dislike statements from a random selection of nouns and proper nouns. [Similar to #1 but with more personalization.]
5. Collect a large quantity of horoscopes and Chinese cookie "fortunes". Select from them at random until 25 "facts" have been accumulated. [Similar to #2 but with more chance of succeeding before death, probably severe interestingness bias but at least the subject is no longer generating the facts.]
Unfortunately none of these methods can deal with a secondary problem, the large universe of facts about you which are true but you don't remember. Certainly those should count in the set of facts about you too!