A good opener from Arden.
ACROSS
ACROSS
9 - Cereal said to cause dental problem (7) - SORGHUM (~sore gum)
11 - Right to exist in the globe, it often weighs heavily on one
(7) - BARBELL {BA{R}{BE}LL}
12 - Dishonourable police officer on count (7) - IGNOBLE {IG}{NOBLE}
13 - Hired to implant eggs, gave new life (9) - RENOVATED {REN{OVA}TED}
16 - American raced around in a vehicle which was not new (4-3) - USED-CAR {US}{ED-CAR<-} (Correction - {US}{ED-CAR*} - See comments)
19 - Shifting target before a race (7) - REGATTA {TARGET*}{A}
20 - Midshipman and others are part of a corolla (5) - PETAL {shiPman}{ET AL}}
21 - Demarcate building which has become weak (9) - MACERATED*
25 - Insisting a lawyer produce the fellow on time (7) - ADAMANT {A}{DA}{MAN}{T}
26 - Exorable to allow nine characters within (7) - LENIENT {LE{NINE*}T}
28 - Ruler measure on Iron (7) - EMPRESS {EM}{PRESS}
29 - A month of work for Paul the predictor (7) - OCTOPUS {OCT}{OPUS}
DOWN
1 - Things are equally intense all along the line (6) - ISOBAR [CD]
2 - Practice air escape (3,3) - DRY RUN {DRY} {RUN}
3 - It is worn to keep people away, reportedly (4) - SHOE (~shoo)
4 - Charm a beast over time (6) - AMULET {A}{MULE}{T}
5 - Shock with an exhortation to let one’s hair down a little more
(8) - BEWILDER {BE WILDER}
6 - Such sweetness is fine (5,5) - ICING SUGAR [CD]
7 - Weakest charge, before the cream had left (8) - FEEBLEST {FEE}{B{L}EST}
8 - Caught between aliens over a period of time and so on…..
(2,6) - ET CETERA {ET} {C}{ET}{ERA}
14 - Was in two minds and left, feeling sick inside (10) - VACILLATED {VAC{ILL}ATED}
16 - One in France put out of the victory stand (8) - UNPLACED {UN}{PLACED}
17 - They plan manoeuvre to find the total energy of the system
(8) - ENTHALPY*
18 - Being farthest it is but a speck among others (8) - REMOTEST {RE{MOTE}ST}
22 - Clubs permit those who are young and inexperienced (6) - CALLOW {C}{ALLOW}
23 - Relationships draw on energy backup system (3-3) - TIE-UPS {TIE}-{UPS}
24 - It is extremely deplorable to be put on trial, one would hate it
(6) - DETEST {DeplorablE}{TEST}
27 - Some eggs are in the carton, it’s to keep them safe (4) - NITS [T]