Pretty much all of the difficulty arises from the transliteration of Greek ψ, υ, χ, and φ, and then inconsistent pronunciations of these letters themselves in loanwords (including pronouncing υ as both /aɪ/ and /ɪ/)!

That's not to say that it's not very tricky, just that the difficulty kind of arises from one core reason.

Edit: OK, one s as /s/ after the c and another s as /z/ between vowels is also tricky and doesn't have to do with Greek.