Applying the German Tank Problem to the age of the universe yields an estimate that the universe will end in another 13 to 260 billion years, far sooner than the predicted time scales of the heat death of the universe.
A related problem: it seems strange to me that life on earth has existed a significant fraction of the age of the universe, when there is nothing constraining it to be so. If our solar system had formed a trillion years from now -- and it seems solar systems will still easily be able to do so then -- things would have turned out here about the same: the night sky would just look different.
What happens 13 billion years from now? False vacuum. Big Rip. An intelligent civilization, perhaps us, figures out a way to destroy the universe. Alternatively, the universe simply becomes inhospitable to life as we know it, which is not unrealistic: the end of the Stelliferous Era.
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