A recent article on The Conversation website looked at idioms that are often misunderstood or misused. People often say the proof is in the pudding, instead of the original saying, which was the proof of the pudding is in the eating. The commonest meaning of proof today is 'evidence', and that meaning is first attested in the OED in the early 13th century. The second meaning of proof in the OED also goes back to the early 13th century, but is a rare meaning nowadays, and that is 'to put something to the test; to test the genuineness or qualities of'. It is this second meaning that is alluded to in the old saying - no matter how good a pudding looks, the only way to see how good it really is is to eat it.
Many people claim that it is this meaning that is meant by the verb prove in the rather puzzling phrase the exception that proves the rule i.e. puts the rule to the test. The writer of the aforementioned article, Simon Horobin, Professor of English Language and Literature at Oxford University, says that it is the word exception that causes the confusion here. Rather than exception referring to something that does not conform to the general rule, it actually refers to something that has been deliberately excluded from the rule. It is an allusion to a Latin legal maxim, exceptio probat regulam in casibus non exceptis, 'the exception confirms the rule in cases not excepted'. Professor Horobin illustrates this by imagining a shop sign that states the exception, 'Open late on Thursdays', which implies a rule that the shop does not open late on the other days of the week.
Other idioms discussed in the article are one fell swoop, off one's own bat and begs the question.