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Lewis Carol noted that a clock that doesn't work at all is right twice a day whereas a clock that loses a minute a day is right every 1.97 years, and by this calculation the broken clock is the better value.
But of course, if we know the clock loses a minute a day, you could derive the current time based on how long ago the clock was set to the correct time, or you could just throw it forward one minute at the end of every day and reset it that way with no reference. The broken clock is just completely useless as a timepiece, though. I think lewis carol was wrong.
I'm pretty sure Carol was being facetious. There's more value obviously in a mechanical thing that works — even if not well — then one that doesn't. The joke is in the notion that we judge clocks based on how well they tell time, which is not a good metric once they deviate significantly from that standard.