Italian is quite similar, but they also occur: ho, hai, and ha (first, second, and third person singular of avere: “to have”) are pronounced identically to o, ai, and a (“oh”, “to the”, and “to”). I’m sure there are others.
There are a handful of homonyms as well: pene can mean “penis” or “pains” (plural of pena) and piano can mean both “soft” (and the instrument, but that’s a derivation) or “story” as in floor of a building.