Solution to 23A has been deliberately left unsolved and is to be answered only by a non-regular / novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
Open for anyone to answer, if not solved by 1 PM.
ACROSS
1 They need to be taught a lesson about failure (6) PUPILS SLIP-UP<=
4 One's c-cross to bear? (6) AFFORD {A}{F-FORD}
8 One street goes around Italian city (7) TRIESTE {1+STREET}*
9 Man! With this braggart, I get most annoyed (7) EGOTIST {EGOTIST+M}*=I+GET+MOST [CA]
11 Estimation of a tax shown to the auditor (10) ASSESSMENT (~ a cess meant)
12 Go to lake and strip (4) PEEL {PEE}{L}
16 A dashing personality? (8) SPRINTER [CD]
18 Sailing east, around Australia (2,3) AT SEA {EAST}*{A}
20 Nitwit knocked back rum bottles only (4) DODO {ODD<=} over {O}
21 According to Spooner, many excelled in swimming event (10) BACKSTROKE (~stack broke to backstroke)
23 One suspect reportedly gets betrayed (4,3) ?O?D ?U? (Addendum - SOLD OUT (~sole doubt to sold out) - See comments)
24 Reason one can't travel abroad to Germany, or a city in Serbia? (4,3) NOVI SAD {NO VISA}{D}
25 Part of cliff or a fjord receding in the distance (3,3) FAR OFF [T]
26 Heard Frank finally got a revolver (6) PLANET {(~plain)PLANE}{goT} Incorrect homophone See comments
DOWN
1 First to finish remaining prunes? (5) PARES (-s)PARE(+s)S
2 Wants to guide chaps playing soccer primarily (7) PREFERS {Pl...g}{REFER}{So...r}
3 That's life, working for a 2 pm -10 pm job perhaps (4,5) LATE SHIFT*
5 Fellow takes time out in tough contest (5) FIGHT {F}{tIGHT}
10 Amateur gets inspired by fantastic career in a team sport (5,4) RELAY RACE {LAY} in {CAREER}*
13 Gradually steal in shop? (6,3) SIPHON OFF {IN+SHOP}* [RA]
19 European dancing in bar - extremely seductive (7) SERBIAN {IN+BAR+Se...vE}*
21 Downright lie! (5) BLUFF [DD]
Reference List
Man = M, Lake = L, New = N, Australia = A, Only = O, Germany = D, Fellow = F, Can = LOO