「ゆうこと」？

Does anyone know what ゆうこと might mean?

I was looking at the profile of a member of a Japanese band and one part has me confused.
It says: 好きなタイプ：ゆうことを聞いてくれる人
ゆうこと is not in my dictionary, but I was thinking it might be like 言うこと, because of the pronunciation.
So that would be "favourite type: someone who will listen to what I say", which sounds believable to me.

But I'm still unsure, so if anyone could help me I'd really appreciate it!

I think you hit the nail on the head, hebiichigo. A while ago, I was told that "yuu" instead of "iu" is one of the most frequent misspellings done by native speakers of Japanese, simply because it is pronounced "yuu".