The Connacht pronunciations of arán vs. aráin could be compared, but this particular example is a bit subtle. The slender version will sound as if it has something of an English consonantal Y following the N. If you’re familiar with a Slavic language, the difference between hard and soft consonants in e.g. Russian is similar to the difference between broad and slender consonants in Irish.
The closest English equivalent might be in the pronunciation of a word like “duke”; a “broad” analogue might sound like “dook”, and a “slender” analogue might sound like “dyook”. Another possibility might be “coupon”, where broad would be “coo-pon” and slender would be “Q-pon”. These English palatalizations would be more prominent than the Irish slender palatalizations, though.
Ok, well in that I hear the "I" certainly. I hadn't got the impression there was a hard and fast rule about "AI" pronouncing both vowels, at least not from the lessons and pronunciations I'd heard so far. Do plurals that change A to AI always pronounce both vowels?
But I don't hear anything particularly palatalized about the "N" at all. Unless I'm mistaken, a palatalized nasal sounds like the Ns in "annual". As that sound comes with a y-glide after it, I'm not sure how that can be accomplished on the final consonant, unless a vowel sound is being added after, or there's another palatalized nasal sound in use here that I'm not hearing.
Both á and ái should have identical pronunciations; the i is there only to show that the next consonant should have a slender pronunciation. There’s some variability in the pronunciation of ai, though.
I did note that the palatalization in that recording of aráin was subtle.
“Annual” has the English consonantal Y sound (IPA /j/), which is stronger than the palatalization of Irish slender consonants. If you think of the pronunciation of the musician Enya’s name (Eithne), that has a slender N followed by a “schwa” — if you clip the schwa, you’ll get a final slender N.