While this is a tiny tiny representation of the total, I have two friends who I know original selected the option not to show their place of birth on their CAN passport. Both said this created so many issues at the border (entering the US, as well as other countries) that they modified their passports to add it back in.
I also have a friend (more of an acquantaince really) who pulled a "plead the 5th" at the US border. He said something like "I don't have to answer that question" to which they responded, "yes, and we don't have to let you into the US of A". So he was sent home. This was a decade ago (at least?) and he still has some sort of flag on his profile related to this that creates problems for him.
My worst experience so far has been travel to Moscow on my previous passport. It took three visits to the embassy to get a visa, lots of paperwork and invitation letters from a hotels between Moscow and St Petersburg. Finally when I landed in the middle of the night in Moscow, single traveller, with a lot of photography gear, the questioning was intense. In addition, my connection to St Pete's was six hours away, by train. My fluency in Russian was as good as his English!!! Ultimately an interpreter had to be called. The immigration guy could not believe that anyone would travel to Russia in March / April for a photo shoot as most of it was still frozen. The only good part about the questioning was that I did not have to spend a lot of time at the railway platform exposed to the cold! Made it to the train. Painful experience at the airport, but well worth the pictures I have.