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ACROSS

 1 New Testament hastened the Christian Era’s flashy arrival (5,8)

 9 Flyers trumpeting less than half of a six-pack? (7)

10 Kind of log ultimately seen near Russian river (7)

11 and 24 1 in a new style (6)

12 I understand Southern bishop’s purview in Florida town (11)

13 It’s about managing corn, amigo! (9)

15 Fear, for instance, is something that might envelop a superhero (4)

17 Dictated legal documents for a fancy hotel (4)

19 Pennants set right in boats (9)

22 Supplying oxygen to metal to break up delay (11)

24 See 11

26 I’m initially pursuing every charge (7)

27 Some cats purr a lot when returning socks (7)

28 OK, acute mix-up involved in sweet drink order—one we evidently observed
in writing three of this puzzle’s clues (4-3,6)

DOWN

 1 “Reptile!” is somewhat derogatory (5)

 2 Baseball team falling short in parts (7)

 3 Sound of a connection when singer comes inside to have a meal (4,4)

 4 Where astronauts are beginning to learn about the proboscis (5)

 5 Budget offering with a bit of nonmetallic mineral in back (6,3)

 6 Show of approval to be announced within fair (3,3)

 7 Text from entrepreneur as I assess large tract of land (7)

 8 Feature of doubloon: especially loud azure quality (8)

13 Farewell appearance has half of us flipped over (2,6)

14 Replace nut’s original letter from Greece—it could be right under your nose!
(9)

16 Animal’s distressed groan in climbing tree (8)

18 Hamilton (at least for now) sent out vessel (3-4)

20 Find yourself on the Internet in unsettled fog? Sure! (3-4)

21 Take control of alternating current, interrupting some of a well-known
sequence (6)

23 Random tiles land in the water (5)

25 Result of leaders in England not shaping up, exactly (5)

SOLUTION TO PUZZLE NO. 3390

ACROSS 1 S(CHROD)INGER + SCAT (chord anag.) 9 LEVI(TICU)S (I cut anag.) 10 [y]BUR + RO (rev.) 11 anag. 12 IMP(OVER)ISH 14 hidden 15 THIR[s]T I.E.-S 18 O + R(ALEX)AM 20 rev. hidden 23 M[err]Y + FAIR(LAD)Y 25 anag. 27 L + EARN 28 BRASS[i]ER-I-E 29 letter bank

DOWN 1 SYLLAB (rev.) + US 2 anag. 3 O + ATH (anag.) 4 IN + COMET + AX 5 G(ESS)O 6 letter bank 7 CORN + ICE 8 TR(OPH)Y (hop anag.) 13 anag. 16 IM(MEDIA)TE (Time anag.) 17 ST(ARLES)S 19 REF + RAIN 21 AND/OR + RA 22 A MULE + T 24 hidden 26 A + STI (rev., &lit.)