1 down: Privates dope Florentine shrink (9)
Playful DA: dope Florentine shrink = gen Italian shrink = genitalia = privates.
25 across: Little looks at newspapers? (8)
Me and a few more liked it lots, others not so much: little looks = gazettes = newspapers.
19 down: Report wise to include dearest sort recently (9)
I loved the aural part of this clue: report wise to include dearest sort = YY to include esterda = yesterday = recently.
21 across: I’m back-to-front describing lair riders (7)
It’s DA everywhere: I’m back-to-front describing lair = AD DA describing den = addenda = riders.