A complete set of minimal pairs for every possible pair of phonemes is quite sizeable.
I copy here the one from Serianni's Italiano (p. 4) for vowels:
i e ɛ a ɔ o u
ɛ pezzo esse
a pazzo fatta pazzo
ɔ fola spola trono botte
o pozzo groppo pozzo pozzo botte
u puzzo pura puzzo puzzo lutto puzzo
(Every word yields the pair when the vowel corresponding to its row is substituted with the one corresponding to its column.)
Probably the most interesting minimal pair here are the ones for e/ɛ (ésse, plural feminine form of esso and èsse, name of letter S) and for o/ɔ (bótte, “barrel” and bòtte, “blows”); notice that in these words the accents aren't usually written down.
Serianni's book has on pp. 6-7 an analogous table for consonant sounds. To just give one example for one of the troublesome ones, take the two phonemes corresponding to the letter z, /ts/ and /dz/: razza (respectively “race” and “ray”, the fish).
Finally, if this is to learn pronunciation, note that in Italian – as in other languages – there happen to be single phonemes corresponding to more than an actual sound. For instance, there is a single phoneme /n/ in Italian, but it corresponds to different allophones: [n] in numero, [ŋ] in angolo.