Across:
1 Had oily (had oily) nuts (= anagram indicator) (had oily = HOLIDAY) with cold (C-) drink (-ALE-) during half-time (HT = -H-T) (HOLIDAY CHALET) in The Swiss Cottage (HOLIDAY CHALET),
10 Palatial (OPULENT) Oxford (O-) bar (pub) is not finished (b) (‘pub’ without ‘b’ = -PU-) – is it time to give up? (-LENT) (OPULENT),
11 One is bound to change pitch with this (VIBRATO) sign (V- sign) from childish type (-BRAT-) inside Number 10 (-I-O) (VIBRATO),
12 Inherits, then goes missing (‘inherits’ ‘then’ goes missing/without ‘then’ = iris = IRIS) from pupil’s place? (place of pupil in the eye = IRIS),
13 Shady type (OCHRE) of leader on (leader ‘On’ = O-) the run (run in cricket = -R-) taken in by revolutionary (Che = -CH-E) (OCHRE),
15 She’s out of whiskies (‘shes’ out of ‘whiskies’ = wiki = KIWI) and fruit for a summer cocktail perhaps (KIWI),
17 Local boozer (SOT) in Minnesota (in ‘minneSOTa’ = SOT),
19 Supernaturalism disregards reprisals (‘supernaturalism’ disregards ‘reprisals’ = untuam = AUTUMN) when Halloween arrives (AUTUMN),
21 Acre on (acre on) settlement (= anagram indicator) (acre on = CORNEA) is in front of one’s eye (CORNEA),
22 Rock (rock MUSIC-) near a (-A-) port (port/left = -L) (MUSICAL) with cats? (Cats = MUSICAL),
23 An overcoat (RAGLAN overcoat) found in River (R-) Lagan (Lagan) is suspect (= anagram indicator) (Lagan = -AGLAN) (RAGLAN),
25 Sort (sort) out (= anagram indicator) (sort = TORS-) tops, overalls, swimming (tops/first letters of ‘Overalls Swimming’ = -OS) (TORSOS) trunks (TORSOS),
27 Mammal (bat) raised (= reverse indicator) (bat = TAB) by Bill (TAB),
29 35 across (so-and-so) has lost heart (lost centre) (‘so-and-so’ without ‘and’ = SO-SO) – is that fair? (SO-SO),
30 Characters in Molloy, a literary (characters in ‘molLOY A Literary’ = LOYAL) offering that’s faithful to others (LOYAL),
31 Body of foreign politicians (DUMA) in tank leaving Katmandu (‘tank’ leaving ‘Katmandu’ = madu = DUMA),
34 Get the message (REALISE) lies are (lies are) unnatural (= anagram indicator) (lies are = REALISE),
35 Report (= homophone indicator) work in a sweatshop (‘sew-and-sew’ = ‘SO-AND-SO’) with vulgar type (SO-AND-SO),
36 They’re taking a break (HOLIDAYMAKERS) from the travel agents presumably (HOLIDAYMAKERS).
Down:
2 Ring (O-) is (-IS-) taken in by sect (cult = -CUL-T) (OCULIST) – the one specialising in visions? (OCULIST),
3 Thought (IDEA) this is integral to seaside alder (this is integral to ‘seasIDE Alder’ = IDEA),
4 Hero removed from chain store (‘hero’ removed from ‘chain store’ = cainst = ANTICS) synonymous with high jinks (ANTICS),
5 Cobh (Cobh) saying (= homophone indicator) (‘Cobh’ = ‘cove’ = COVE-) around resentment (around ‘ResentmenT’ = -RT) (COVERT) is not going to make it into the papers? (COVERT),
6 Labs (labs) condemned (= anagram indicator) (labs = ALBS) by religious outfits (ALBS),
7 Joy (ELATION) gets into ale (into ale) brewing (= anagram indicator) (into ale = ELATION),
8 Old (-O-) top (-LID-) found in fodder (H-AY) is concerning (concerning/about = RE-)? Put in piles (-SORT) (HOLIDAY RESORT) for those taking their leave! (HOLIDAY RESORT),
9 Take to the road – away (HOLIDAY) team has to cope with it (SEASON) (HOLIDAY SEASON) over the Christmas period (HOLIDAY SEASON),
14 Rest period (HOLIDAY) for those starting on all sides today (HOLIDAY on all sides of today’s grid),
16 Miracle man loses relic (‘miracle man’ loses ‘relic’ = maman = AMMAN) from middle-eastern capital (capital of Jordan AMMAN),
18 Criminal (CO-N) admits starting on landing (starting on ‘Landing’ = -L-) officer (-O-) (COLON) – it’s the sort of thing you normally see half way through a sentence (punctuation mark in a sentence = COLON),
20 One of those with a habit (NUN) found in pedestrian underpass (found in ‘pedestriaN UNderpass’ = NUN),
21 Pet (CAT) raised (= reverse indicator) by Santa Claus inside (raised by ‘sanTA Claus’ inside = tac = CAT),
24 Old force associated with state police known by its letters (the GESTAPO administered by ‘secret state police’ / SS) and odd (= anagram indicator) postage (postage = GESTAPO),
26 Shake (SHUDDER) shillelagh at both sides (‘ShillelagH’ at both sides = SH-) at the helm (rudder) starting off (r) (‘rudder’ without ‘r’ = -UDDER) (SHUDDER),
27 Cork (TOP-) heads from Eyeries, Kinsale, Ardgroom (heads from Eyeries, Kinsale, Ardgroom = -EKA) (TOPEKA) found in state capital (TOPEKA is the capital of Kansas),
28 Cream (BAL-M) covers tops of strawberries and (tops of ‘Strawberries And’ = -SA-) (BALSAM) something that’s naturally fragrant and soothing (BALSAM),
32 Horrified losing order (‘horrified’ losing ‘order’ = hifi = HI-FI) for sound system (HI-FI),
33 In Arizona, use a lot (in Arizona/American use a parking lot = PARK a car) in Phoenix, for example? (Phoenix PARK).