Thank you to Hypnos. Definitions are underlined in the clues.
Across
1. Explorer appreciated source of medicine in medical facility (6)
TASMAN : TA(thank you!/expression of appreciation) + [ 1st letter of(source of) “medicine” contained in(in) SAN(short for “sanatorium”/a medical facility) ].
Answer: …, Abel, Dutch explorer.
4. Prominently publish odds on disgraced Swiss official losing face (8)
SPLATTER : SP(abbrev. for “starting price”/the odds at the start of race of a particular horse winning the race) + “Blatter”(Sepp, former disgraced Swiss president of FIFA, found guilty of corruption and fraud) minus its 1st letter(losing face).
9. Treatment for one largely dull, small swelling (6)
NODULE : Anagram of(Treatment for) [ONE + “dull” minus its last letter(largely …) ].
10. Instant record of events showing offhand heavy drinker grabbing husband (8)
SNAPSHOT : SNAP(offhand/without prior thought or consideration) + SOT(a heavy drinker/drunkard) containing(grabbing) H(abbrev. for “husband”).
11. With no end of hoo-ha, suspect decrease in digs, say (9)
RESIDENCE : Last letter of(end of) “hoo-ha” deleted from(With no …) anagram of(suspect) “decrease in“.
Defn: …/accommodation.
13. Time taken by a number to comprehend good Latin American dance (5)
TANGO : T(abbrev. for “time”) plus(taken by) A + NO(abbrev. for “number”) containing(to comprehend) G(abbrev. for “good”).
14. Liar’s outfit is shoddy – typical of one making advances? (11)
FLIRTATIOUS : Anagram of(… is shoddy) LIAR’S OUTFIT.
Defn: …/approaches made to someone to initiate sexual or amorous relations.
18. Difficult American turncoat with no independent source of pictures? (11)
ILLUSTRATOR : ILL(difficult/presenting difficulty as in “ill-timed”) + US(abbrev. for things American) + “traitor”(turncoat/betrayer) minus(with no) “I”(abbrev. for “independent”).
21. Thing used by jewellers to examine ring, we hear (5)
LOUPE : Homophone of(…, we hear) “loop”(a ring/a length of, say, thread formed into a ring).
22. Only depot sadly with nothing for new miniature dog (3,6)
TOY POODLE : Anagram of(… sadly) “Only depot” with “o”(letter representing 0/nothing) replacing(… for …) “n”(abbrev. for “new”).
24. One doing twist in flexible roles, nothing less (8)
SWINDLER : WIND(to twist/to coil round) contained in(in) anagram of(flexible) “roles” minus(… less) “o”(letter representing 0/nothing).
Defn: …/conning somebody.
25. Position adopted among hardest ancestors (6)
STANCE : Hidden in(among) “hardest ancestors“.
26. Legal authority in New York worked on treaty (8)
ATTORNEY : Anagram of(worked) ON TREATY.
27. Excessive amount found by academic about The Origin of Species? That’s probable (4-2)
ODDS-ON : OD(abbrev. for “overdose”/an excessive amount, of, say, drugs) plus(found by) DON(an academic/a lecturer at, say, a university) containing(about) 1st letter of(The Origin of) “Species“.
Down
1. Belief almost widely prevalent in holiday destination (8)
TENERIFE : “tenet”(a belief/a doctrine, in say, a religion or philosophy) minus its last letter(almost) + RIFE(widely prevalent/everywhere).
Defn: …, the largest island of the Canary Islands in the Atlantic Ocean.
2. Team supported by country lacking a finesse with the ball? (8)
SIDESPIN : SIDE(one of the teams in a competition) placed above(supported by, in a down clue) “Spain”(the European country) minus(lacking) “a“.
Defn: In billiards and snooker, a horizontal spin given, skilfully/with finesse, to the cue ball.
3. A place selling cheese in turn got in a bad way (5)
AILED : A + reversal of(.. in turn) DELI(short for “delicatessen”/a place selling delicacies, such as cheese).
5. Play opens dourly in a laboured style (11)
PONDEROUSLY : Anagram of(Play) OPENS DOURLY.
6. A mixture of peas and tripe for an early dish? (9)
APPETISER : Anagram of(A mixture of) [ PEAS plus(and) TRIPE ].
Defn: …/a small dish of food before the main course of a meal.
7. Money required around a hotel on island for Middle East dish (6)
TAHINI : TIN(slang for “money”) containing(required around) [A + H(letter represented by “hotel” in the phonetic alphabet) ] placed above(on, in a down clue) I(abbrev. for “island”).
From: 
to:
8. Restrict the supply of liquid in rota (6)
RATION : Anagram of(liquid) IN ROTA.
12. Some not present presumably? That’s somewhat stupid (3,3,5)
NOT ALL THERE : [NOT ALL](only some] THERE(present at that, whichever, place).
15. Fine line shown in proposal for one making late arrival on the square? (9)
TAILENDER : [ AI(A1/the best quality/fine, with the Roman numeral substitution) + L(abbrev. for “line”) ] contained in(shown in) TENDER(a proposal/an offer in response to, well, a tender).
Defn: The batsman in a cricket side who is the last in to bat/the last batsman to enter the square/the rectangular central part of a cricket field used as the pitch between the wickets – rectangular square?
16. Undergraduates, maybe, of French engaged in antics (8)
STUDENTS : DE(French for “of”) contained in(engaged in) STUNTS(antics/unusual deeds to attract attention).
17. Brother in France adopting English at home gets total latitude? (4,4)
FREE REIN : [ FRÈRE(“brother” in French) containing(adopting) E(abbrev. for “English”) ] + IN(at home/not out of the house).
19. Request to enter a filming location in US state (6)
ALASKA : ASK(to request/to call for) contained in(to enter) [ A + LA(abbrev. for “Los Angeles”, in which Hollywood, where many US films were made, is located).
20. Overly formal type for all to see amid trips abroad (6)
PURIST : U(the UK certification code for movies that allows patrons of all ages to see/watch) contained in(amid) anagram of(… abroad) TRIPS.
23. A group in part of autumn commercial (5)
OCTAD : OCT(abbrev. for “October”, a month in/part of the autumn season) + AD(abbrev. for “advertisement”/a commercial/promotional material).
Defn: … of eight.
Thanks Hynos and Scchua!
Rectangular square-interesting 🙂
Liked SPLATTER and RESIDENCE.
Scchua, you’ve misspelled the setter in your header.
TAILENDER & SWINDLER took some working out. Didn’t understand the “on the square” bit but, assuming it is a cricket reference, no surprise there.
Re SPLATTER I didn’t know SP as a betting abbreviation so took it to be the odd bits of SEPP. Scchua’s parsing much less clunky so I thank you.
Also tried to wrestle some kind of punning Albert Square reference into TAILENDER. Ah well.
Thanks Hovis. Correction done.
Salad @3: you are not the only one to have been wondering about Eastenders! Sadly, a DNF as I didn’t know TASMAN was an explorer; makes complete sense but, without the knowledge, I couldn’t get it from the wordplay. TA for appreciated didn’t come to mind. I did like the definition for SWINDLER. I’m wondering – does tin ever get used for money outside of crosswordland?
Thanks Hypnos and scchua
I enjoyed this a lot with SPLATTER, SWINDLER, TENERIFE & TAILENDER my podium choices.
Many thanks to Hypnos and to scchua.
Some reverse parsing required for 4a due to lack of sports knowledge which is apparently a necessity in the Indy world! OCTAD was new to me but fortunately very well clued.
Think my favourite was NOT ALL THERE which made me laugh.
Thanks to Hypnos and to scchua for the review.
One of those rare days when SPLATTER is a good thing. Thanks, both.
Can TAHINI be called a dish? Certainly it’s an ingredient in hummus, which is a dish
I thought this was a little over convoluted with too many one letter subtractions although in hindsight they were all indicated fairly.
Only got TAILENDER from the crossers as nho but that’s nothing new with sports terminology for me.
I’m just old enough to remember when certain pubs and clubs had an SP bookie (usually an old soak) who would take your bet without you having to leave your local to place it. Although I certainly wasn’t old enough to have been a legal patron of the premises 😉
Thanks Hypnos and scchua
Definitely a two-session puzzle but none the worse for that, although there were a few we couldn’t parse and we only parsed TAILENDER as an oblique reference to Eastenders – odd, because we usually spot cricket references.
We thought 12dn wasn’t quite up to Hypnos’ usual standard, having ‘not’ in both clue and answer. But there was plenty to like, including SPLATTER, RESIDENCE, FLIRTATIOUS and TENERIFE.
Thanks, Hypnos and scchua.
Square is legit. The square is the central part of cricket field which includes various rectangular pitches in various states of preparedness. A centre square with, say eight pitches would be very square.