My life took a new peacock

This page from my Teach Yourself Hindi book is a beautiful illustration of a difficulty that I--and perhaps you too?--struggle with all the time in learning Hindi.
At the top of the page you find the last few lines of a dialogue between Dadi-ji (grandma) and Pratap. He's telling her about how seriously he's taking his Hindi studies, and she's trying to be encouraging. (Such a good Desi boy!) Acknowledging the authors' and publishers' full copyright credit, I reproduce the key lines here.

प्रताप     जिस दिन मैंने हिंदी सीखना शुरू किया, उसी दिन से मेरे जीवन में एक नया मोर आया.
दादी जी [ख़ूब हंसकर ] अरे "मोर" नहीं बेटे, "मोड़"! "एक नया मोड़"!
प्रताप    [झेंपकर ] माफ़ कीजिए दादीजी, ऐसी उच्चारण की गलतियाँ मुझसे हमेशा हुआ करतीं हैं !

[Pratap  Jis din maine hindi sikhna shuru kiya, usi din se mere jivan mein ek naya mor aaya.
Pratap   From the day I began learning Hindi, my life took a new peacock.]

[Dadiji  [khub hanskar] Arre, "mor" nahi, bete, "mod"! "Ek naya mod"!
Grandma [laughing heartily] Hey, not "peacock," child! "A new turn"!]

[Pratap  [jhempkar] Maaf kijie dadiji, aisi uccharan ki galtiyaan mujhse hua kartin hain!
Pratap   [embarrassed] Forgive me, grandma, these pronunciation mistakes are forever happening with me!]

The mistake lies in मोर (mor/peacock) versus मोड़ (mod/turn). The distinction is far, far subtler than it looks on the page. Look closely at these two words, and you see the one-letter difference right away: र looks clearly different from ड़. A comparable pair in English--in terms of appearance--would be something like pen versus pet. Easy. However, as Hindi speakers know, and native Hindi speakers really know, र and ड़ sound very nearly alike--particularly to the unaccustomed Western ear. This is my book's description of the two sounds:
"र as in 'roll'"
"ड़ a flapped hard 'r'--the tongue makes a da sound as it moves past the palate"
If only it were that simple. To my ear, the "r as in roll" is actually, well, rolled a bit, as in Spanish, so that it sounds halfway between r and d. And the "flapped hard 'r'" is softened a bit. So they approach each other from both directions, and--I'm telling you, after many hours of listening carefully to Hindi spoken in Bollywood movies, anyway--they sound alike to me.
The point I've worked toward so laboriously: there are lots of sounds like these two in Hindi, pairs and sometimes (for example, त, ट, थ, and ठ) quadruplets!
Telling them apart requires two things: practice (and more practice!), and a large and ready enough vocabulary that when someone says "My life took a new peacock," you realize quickly that the speaker meant something else, and it must be ____.
Good luck to you and me and all Hindi learners as we learn to hear and pronounce these subtle differences correctly!