Now, this is Dimitris Almyrantis asking, so he deserves some politics in his answer!
“Acknowledged”? Well put, because mutual intelligibility is often more about identity politics than about communication. As in the cause célèbre of the PM of Macedonia bringing along an interpreter to his meeting with the PM of Bulgaria.
Greeks acknowledge idioms where anyone else would say “dialect”, and “dialects” where anyone else would say “that’s a different language”. For the same ideological reasons that people on Quora grouse that there’s no such thing as Northern Greek, and that I got harangued once for saying I work on Middle Greek. At least it never got as bad as Turkey, where linguists were discouraged from researching dialects at all.
Tsakonian is within Greece, and it’s so, so a different language, it’s not funny. Check out Tsakonian song online for an example. (And hang out there, I’ve written some neat stuff in my time.)
Of the other acknowledged “dialects” of Greek: Actual Cypriot, as opposed to Standard Greek with a nasal sing-song accent, is not mutually intelligible. Griko in Italy can be intelligible, though I think the moribund Calabrian variant is much more of a challenge. Pontic is not mutually intelligible, but it can be picked up (as Dimitra Triantafyllidou has); Mariupolitan ditto. [EDIT: Forgot Cappadocian. Way more different than Pontic.]
Cretan is deemed on the borderline of dialect and “idiom” in traditional Greek dialectology. It does less phonologically odd stuff than Cypriot, and Renaissance Cretan is approachable, but I agree with Bob Hannent: the genuine article is going to be a challenge for Standard Greek speakers
Within Greece, what you have left are “idioms”. The mutual intelligibility of those can be overstated.
Northern Greek, with its raising of unstressed /e, o/ to /i, u/, and its deletion of unstressed /i, u/, is not that interesting morphologically or lexically—but yes, phonetically it’s… something else. That’s what happens when you get rid of half your vowels. I presume that’s what you were exposed to in Northern Euboea, Dimitris.
(If you were in Kymi, you were exposed to a relic dialect related to Old Athenian, preserving /u/ for ancient upsilon. If you were anywhere else in Southern Euboea, what you heard was Arvanitika, and it’s no wonder you didn’t understand it.)
The 2004 international conference on Greek Dialectology happened in Lesbos. Someplace in Mytilini town, a local has scrawled some bon mots in the local dialect on the arch outside his café. Lesbos also has a Northern Greek dialect. So you can picture three internationally renowned Greek dialectologists (OK, two plus me), standing outside the café to the merriment of the locals, staring at the bon mots and trying to fill in the vowels.
The maximum meltdown happens in Samothrace, which has stuck with me because I honestly had no idea what the hell was going on when I first encountered it (in a phonetic transcription of WWI POW’s, published by Werner Heisenberg’s dad, August). The grammar of Samothracian I have, annoyingly has no sample texts.
So you’ve got Greek with half the vowels missing, right? OK.
Now take away all the r’s as well.
mavros “black” > mavwus. riɣani “oregano” > jiɣaɲ. anθropos “person” > aθjipus.
There’s a thesis on Samothracian grammar here: ονοματικό και ρηματικό κλιτικό σύστημα. Read the example sentences out loud to yourselves, and tell me you’d understand them…