In the phrase the verb dedicato is probably implicit. Saying
ai miei genitori, il Papa e Madre Teresa
would only mean that the Pope and Mother Theresa are my parents, with no ambiguity whatsoever. In this case it's the grammatical number that makes the difference:
ai miei genitori, al Papa e a Madre Teresa
will convey the correct information. If I want to dedicate my book
*ai miei maestri, colleghi e allievi
I'll choose this form rather than the clumsy
*ai miei maestri, ai miei colleghi e ai miei allievi
The slight ambiguity is immediately cast out, because no one can be master, colleague and pupil of the same person.
Also the article can get into the matter:
a mamma, papà e nonna
would be correct. Note that nonna wants the article in some variant of Italian (a nonna is more Central than Northern Italian). But, with articles,
alla mamma, al papà e alla nonna
tends to require repeating the preposition. The article is not compulsory, but if used the preposition becomes somewhat necessary in front of all terms. I'm not saying that
alla mamma, papà e nonna
is ungrammatical, but it doesn't sound right to my ear. If the gender is the same as in
alla mamma, zia e nonna
it could be right, but leaving a small ambiguity as whether my mother is also my aunt and grandmother. So, when the article is involved, repeat the preposition.
Similarly one will tend to say
andrò al mare, al lago o ai monti
because one term is plural and the others are singular; again, andrò al mare, lago o monti is not good to my ear. On the other hand
andrò a Rimini, Riccione o Igea Marina
can avoid repeating the preposition, but andrò a Rimini, a Riccione o a Igea Marina would be good as well. Here no article can be used, of course.