FT 12,889/Mudd

This puzzle seemed, frankly, a little underwhelming compared  to Mudd’s usual standard. Not that there is anything wrong with it, per se; just seems a tad light on imagination or inspiration. I suppose that’s the down side of publishing setters’ identities – it can start to frame certain expectations in the longer run.

Across
1 DESERT – double def’n.  I wasted a minute or so here, looking for an answer ending in sere (“dry”).
4 DRESSING – A “saucy” surface reading, if you’ll pardon the pun.
10 SEA(U)RCHIN[-g]
12 REED – Deer(rev)
13 SEWAGE FARM – E(nergy) in (a few grams)*
15 TRAIPSE – (pirate)*
16 KA,RATE – I’m willing to indulge “chopping” as the definition here, but the leeway is only because it clearly works best with the intended surface.
19 S,TENCH
21 H(ADD)OCK – “reckon”=add, as in a ready-reckoner.
23 PIL,LOW,CASE – Lip(rev), “blue” = mopey/low, “instance”=case (of).
25 CHIN[-a] – put me in mind of the old (and probably politically incorrect) barb; “He’s got more chins than a Chinese telephone directory”.
27 EG,RE,T
28 ANALOGISE (lose again)*
29 PE(AGREE)N
30 COCK UP – double def’n. As in the catchphrase of Geoffrey Palmer’s character in the Reggie Perrin series. “Bit of a cock up in the […..] department”.

Down
1 DISCRETE – homophone of  “discreet”.
2 SPARE PART
3 RARE – double def’n.
5 RAN,SACK
6 SLAVE TRADE – (dealers + VAT)*
7 IN,DIA[-gram]
8 [-i]GLOO,MY
9 WHEEZE – double def’n.
14 SPIN DOCTOR – a clever idea, but perhaps too transparent?
17 TOO,TH(P)ICK – gets my vote for the clue of the day.
18 SKIN DEEP
20 HECTARE – (teacher)*
21 HUSS,A,R
22 UP,KEEP
24 LARVA – homophone of “lava: (which, I would pedantically point out, is only “hot stuff” in its molten state).
26 POLO – double def’n.