Fridays are always hard. The first answer I put in was for 14d (part of some strippers' attire); I thought it was an item worn on the bottom, but it turned out to be one worn on the top... or rather, attached to the top. But I didn't properly figure that out till later.
The first but I finished was the bottom left corner. I got 51d (crescent moon feature) right away; Dad didn't. I told him he hadn't read enough fantasy novels. 44a (Far-off discoveries in astronomy) came to me suddenly; I think it was because these sorts of discoveries are brand-new and have been in the news a lot. (Hint: Places that might support life in other parts of the galaxy.) Once I got that, 37d (get rusty) was obvious to me (Hint: Literally rusty, scientific term). Then I got 50a (russets, often); a type of potato that often shows up in crosswords. I got 45d (it's big in Bordeaux) next, I think; it's a French word I see more often in the crossword than I ever did in my French classes... well, I saw it a lot in the 19th century poetry class.
Though I'd never heard of the song "Beautiful Boy (Darling Boy)" I now had enough letters to figure out 48a, a well known singing mom. Then 53d and 62a were easy; they're the first and last name of 48a's son.
From there, I got 52d (scramble); one of those common crossword puzzle words for a mix of stuff. I also got 36d (formative), as in the work of a scholar or researcher. I think that's also when I got 38d (pop-top spot); think of something fizzy that you open. 36a ("See if I care!") was easy at that point, being that it's also a refrain from a song.
I forget when exactly I got 27d (tiny opening in a leaf) but it's a scientific term. I also got 31a (avow); it's two words, and something you might do on a witness stand. I figured out 34a (Auto marque of the 1980s-90s); it's a cheap car make, so dressing it up with a fancy clue was misleading. I was delighted to find that my (unwritten) guess for 32d (spinner) was correct; it's something you might put a garden hose or a movie film on.
This was the point at which I called Dad, who was doing the paper puzzle. He'd barely started (having only just gotten the paper), and agreed that it was a royal pain. After some chatting about the bits I had done, we moved over to the bottom right corner. He'd put in someone I'd never, ever heard of for 61a (legendary Spanish bullfighter) so I won't tell you that here. I'd already gotten 59a (fragrant white wine); it's a German region as well. I'd also gotten 46a ("Perpetual Peace" thinker), a German philosopher, from one of my initial guesses, 30d (Dyeing art), a lovely African art form done with wax patterns on cloth. I'd also gotten 41d (volcano in a national park); it's in the Pacific Northwest. 49a (...but no more like my father / Than ___ Hercules"; Hamlet) came to me in a flash, in David Tennant's voice; I've always liked analogies. With all of those, I got 42d (understanding) which is a negotiating term, and one that always makes me think of a treaty group of World War I.
Dad gave me 55d (till compartment); it's a dollar amount, as cash register tills are sorted. That gave me 63a (ropes in); it's what a hunter might do to a bird, or a con artist to a mark. 57d (bit of pottery) then turned out to be a Spanish cooking vessel. I also got 56d ("The race ____!"); it's what an announcer would cry as it begins... and more likely for a space race or political race than for an athletic one. 54a (Secured the rights to) was quick, then; think of how a movie producer would get rights from a writer.
40d (idealist); as in a book by Thomas More. 40a (fault finders?) as in tennis. 43d (fuddy-duddies) turned out to be a variation of an adjective; I thought it was clunky. (But there you are - now you have all the letters for 61a, the one I mentioned not knowing.)
28d (some cheeses) is that Dutch cheese (plural) that shows up in the puzzle at least once a week. 29d (Its uniform includes a red serge tunic and a Stetson; abbr) is exactly the North American police force you're thinking of; now remember their initials.
Dad inadvertently gave me 33a (They may have your number) directly, for which I scolded him. It's a type of thing you carry in your wallet. From there I got 23d (kind of boot); it's one that you'd use in the snow, with binders. 27a (it drops on the way home) has to do with baseball, and you might have to stretch your brain a bit on that one; I did.
Moving over to the upper-right corner, I complained to Dad that it was clear I'd filled in 14d (Part of some strippers' attire) incorrectly. He told me that it was something attached to the bosom wear I'd been thinking of. Aha! That confirmed my initial thought on 16a ("So chic!") but if I were just using that word in a story, I'd do it with seven letters and put an H on the end of the first of those three words. 12d ("More than a turf battle") is a dangerous ongoing conflict in some urban neighborhoods. That gave me 9a (What can be a turnoff?); it's a gadget you'd use to stop the flow of water. Also got 9d (breaks down); as in crying. From there, 18a (aids to privacy); you'd put them over your windows. 13d (Cigarette brand that once used the slogan "Not a cough in a carload") annoyed me as a vehement anti-smoker; a better clue might have been "Precious metal for the Aztecs."
I guessed 11s (Mother of Romulus and Remus) based on the other letters. Then I got 20a (Ricky ______, frontman for bluegrass' Kentucky Thunder) as one of those pop culture things that sticks in your head. Shrugged over 10d (Annual journalism award) but hey, I'd gotten it from the letters.
Moving over to the top left! 7d (Hall with a posse); a late-night talk show host from the 80s-90s who was a whole lot of fun. 8d (Capital that was the scene of 2009 mass demonstrations) I more or less got without Dad, but I'll tell you his hint - it's in a Middle Eastern country that bragged of having nuclear power during Dubya's administration. My thought for 19a (sire) was on the right track when I thought of fathers, but not correct; I was thinking science, but the answer was more Biblical. That gave me 1d (high and low indicators) as in meteorology. 2d (Part of England in the time of Alfred the Great) came to me; not a place so much as a part of government. Then I got 1a (question the morning after); it's what you might say after a bender, and was recently used as part of a con on Burn Notice. 3d ("_______ that!") gave me pause, but I got it on the letters. As one word, it's the title of a song that 53d might sing. 4d (cut); a copy-editing and proofreading term. 15a ("That makes two of us") is a two-word phrase for agreement.
21a (Fassbinder film "___ Fear Eats the Soul") I got on the letters and still doesn't make sense to me. 5d (pique); as in appetite. 6d (fervor) as in warmth.
I think I've covered everything!
For all the answers, and more about that Spanish bullfighter:
