Here is Mudd in fine form. I found 16D difficult and still do not quite see how “go” is clued.

Across
1. HARMLESS - ARM (weapon) + L (left) in HESS (Nazi). Great surface!
5. PARODY - ROD (stick) in PAY (the money)
9. TURNIP - URN (vessel) in TIP (suggestion)
10. TAILSPIN - anagram of ITS PLAIN
11. PARKING LOT - [c]AR + KING (head) in PLOT (area of land)
12. BULL - double definition
13. BIKINI - BIKIN[g] + I
15. RAG TRADE - TRAD (conventional) in RAGE (fashion)
18. INDIANAN - DIANA (girl) in INN (pub)
20. DRY ROT - DRY (boring) + ROT (nonsense)
21. AGOG - A (a) + GOG (giant statue)
23. COMPARABLE - COM (as in .com) + PARABLE (story)
25. MACAROON - CA[ke] in MAROON (shade)
26. ENROBE - BORNE (carried) backwards + [tabl]E
27. CHASTE - T (time) in CHASE (hunting ground)
29. ESTRANGE - anagram of SET + RANGE (roam)

Down
2. ADULATION - AD[ie]U + O (love) in LATIN (which was once spoken)
3. MINSK - S (seconds) in MINK (fur)
4. EXPANSION - EX (old) + PANS (vessels) + NOI (no-one) backwards
5. SETTLER - anagram of LETTERS
6. POINT - double definition
7. RASPBERRY - cryptic definition
8. DRILL - double/cryptic definition
14. ISINGLASS - I (I) + SING (grass) + LASS (girl)
16. GODPARENT - GO (?) + anagram of PAD + RENT (money paid regularly)
17. DOODLE BUG - DOODLE (idly draw) + BUG (error)
19. NOMINEE - NO MINE (unable to dig for gold) + E (energy)
22. GRAPH - hidden word
23. CLONE - L (line) in CONE (tapering object)
24. AORTA - O (Impasto’s ultimate) in ART (painting) + A (a)