It's happened to me on both the listening end and on the speaking end, when I have tried to speak French, Spanish, or Italian.

Very commonly, it's a vowel in the middle of a word which, when changed, gives a totally different word that does not make sense.

1. Easy to understand

Somebody tells me he is going to get his bathing suit because he is "going to the bitch."

2. Harder to understand

A guy with a thick Southern accent asked me, "Have you seen Beale?" There is a guy named Bob Beale in our group, and I think that Bob Beale must be the one who he is asking about. A moment later, Bob Beale comes by and I tell the guy, Here he is. The guy who asked the question in the first place makes it clear he was not looking for Bob Beale, and then he emphasizes, "No. Not Beale. I'm looking for Beale Graham, by which he means Bill."

I've had people ask for a pin, by which they meant pen. Two very different things.