Any version of "The Liberals are an alternative to the Conservatives." Given that the Liberal record under Chretien / Martin is actually to the RIGHT of the Harper Conservatives on a range of issues, including child care and Kyoto (ie, the Cons have done nothing of substance while the Liberals did nothing at all), the only people who see the IggyLibs as an alternative to the HarperCons are gullible people who haven't been paying attention.

Are you kidding? You're asking people who work with the public what's the dumbest thing they've heard people say? Where do we even begin???

Here's 2 that come to mind:

We get a lot of mileage at work from the various dumb stuff a co-worker says. For example, one girl was talking about her twin brother. Doofus pipes up, "oh, are you identical twins?" When we all started to laugh, she insisted that male and female twins could be identical ... couldn't they? I was like, "um, what makes boys different from girls, do you think?"

The other classic Doofus story was when she was telling me about the One-Ton Tomato song. I had no idea what she meant until she started to sing it. Recognizing the tune, I said, "do you mean 'Guantanamera'?" It wouldn't have been half so funny if she hadn't kept insisting that no, it wasn't a parody, and yes she was absolutely sure that the words were "one ton tomato." Even Googling it couldn't convince her, but I nearly busted a gut when Wikipedia referred to it as "the most famous song to ever come out of Cuba." [Not being one to concede defeat, I went home, started downloading, and made her a CD of 16 different versions of Guantanamera ... none of which used the word "tomato"]

Thought of another one:
I spend a bit of time helping a patron find a copy of Mein Kampf. Upon pulling it from the shelf and showing the thick volume to him, he flips through it, looks at me and says, "don't you have one with pictures?"