To some extent, we know how sounds varied between ancient Greek dialects: the Aeolians lost rough breathings but preserved digamma, for example, while the Attics changed many of their long alphas into etas.
But apart from alphabet changes, do we have any evidence of how dialectal pronunciation differed? For example, even if all dialects used theta to write the first letter in θεος, I doubt they all pronounced that theta the same way: at some point it shifted from a plosive to a fricative, and that can't have happened everywhere at the same time.
Writing could potentially give evidence: for example, if X dialect inscriptions tend to substitute hypsilon for iota, we can assume
/i/ were merging. Similarly, if a comedian has a character from Y island say "ουάναξ", then Y dialect probably preserved the digamma even if they didn't write it. However, I don't know of any actual examples of this.