What happens if you don't change the water filter often like in a Cuisanart coffee maker which also filters water?

Don't worry if you have drank unfiltered water. Some people like to drink tap water because they say it has more minerals. In your case, the water you drank from the coffee maker is already boiled. So that makes it much safer than drinking directly from the faucet. If I were you, I won't even replace the filter since the water get boiled anyway. But that also depends on where the source of the water. But the only possible negative outcome is mineral build-up in the coffee machine.