The well-known examples of ambiguity in natural language mostly stem from polysemy (especially across word categories), viz. Time flies like an arrow. In the “advanced” semantics & pragmatics class now being taught at the linguistics department I’ve become more attuned to the room for nuance in semantic (sometimes called thematic) roles, especially in Finnish.
One aspect of this is that many undergoer-roles are expressed with the accusative case which, morphologically speaking, doesn’t independently exist. By this I mean that Finnish isn’t considered by Fennicists to have an accusative case but to instead mark direct objects with the genitive (perfect aspect, söin omenan – I ate an apple) and partitive (progressive aspect, söin omenaa – I was eating an apple) cases. But from a typological (comparative linguistics, if you will) point of view, these together with the special word forms of personal pronouns (minut, sinut, hänet, meidät, teidät, heidät) constitute an accusative case.
This leads to entertaining ambiguities between possessives and objects. My favourite example is from an actual headline from some years ago:
Mies ampui vaimonsa kännykän haulikolla
Man shoot+imperf wife+gen+poss(of wife by man) mobile-phone+gen shotgun+adessive(“with”)
Man shoots wife’s mobile phone with shotgun
Some of the ambiguity is present in the English translation as polysemy, but notably here both “wife” and “mobile phone” are in the genitive, so either one (or neither!) can be taken as the direct object. If the mobile phone is a possessive form, the shotgun is naturally a special function present in it. I’m sure there would be demand for something like this in the market. Thus we may read:
The man shot his wife’s mobile phone with a shotgun
The man shot his wife with the shotgun function in his mobile phone
The man shot (something) with the shotgun function of his wife’s mobile phone
Additionally:
The man shot (used as ammunition) his wife’s mobile phone with a shotgun
The man shot (used as ammunition) his wife with the shotgun function in his mobile phone
Of course, this is a bit pathological – mostly syntax/morphology as semantic marking is sensible business.