A broken clock is right twice a day.
My informant first heard this proverb in the fall of 2010. She cannot remember who told it to her or the context that she first heard it in, but she liked the phrase enough that it stuck with her. She generally says it in a sarcastic, playful tone when arguing with one of her friends and the friend makes a correct point, but my informant thinks that her friends overall argument is flawed. She also uses it when someone who normally gets answers incorrect, answers something correctly. She believes that the proverb means that even unreliable witnesses can be correct, and should be taken seriously despite their bad track record.
My informants explanation makes sense, but given the context that Ive heard her use the phrase in, Im not sure its the best explanation. My informants interpretation implies that when she uses it, she is trusting someones opinion despite his or her tendency to be incorrect. However, given her cheeky tone and the playful atmosphere in which she says the proverb, it seems like the proverb is used to make fun of the person it references, not imply confidence in them. I believe that the proverb implies that sometimes people are right coincidentally or on accident, and that does not mean that they can be or should be trusted to know what they are talking about. A broken clock tells the right time twice a day, but theres no way to know if you are looking at it at exactly the right time. Despite its accuracy in those two specific situations, one cannot trust a broken clock. Likewise, one should not trust someone who is consistently wrong, even if they occasionally say something true. This proverb reflects a distrust of accidental truth.