Barry Silk’s (author of this puzzle) are usually a bit more approachable and this is no exception.  Themeless, of course.  Here we go:

19-Across 1964 Album that was #1 for 11 weeks:  And who else could have had a hit that topped the charts for that long back in ’64?   If you know the group, you know that last word of the answer.  And this was their first smash album, so does that help with the first two words?

2-Down Car ad catchphrase:  Not car ads in general, but a specific brand.  Is there an 21-Down in here?

55-Across Jack regarded as an object of devotion:  Not Jack ______.  Not even capitalized if it weren’t at the beginning of the clue.  No, not apple jack, though I’m sure it has many devotees.   Not religious devotion either.

46-Down Curia _____ :  And where is this Pope being assisted?  No, not the Vatican, but close by.

53-Down Flat sign:  No, not a flat tire.  This kind of flat is a lot roomier.

27-Down W., once:  Yeh, that Dubya.

43-Down Mascot since 1916:  Maybe he should have been the mascot for the Mets from ’62 to ’65!

37-Across 3-D Picture producer:  Normally seen on a much small image than you might think of off the bat.