A bit more difficult than the usual IoS, I thought. Thanks to Gila. Definitions are underlined in the clues.
Across
1 Leather overalls for men (5)
CHAPS : Double defn.
4 Cops in California travel around with special toys? (7)
LAPDOGS : LAPD(abbrev. for the Los Angeles Police Department, cops in California) + reversal of(… around) GO(to travel) plus(with) S(abbrev. for “special”).
Defn: Small breeds of dogs.
9 A world-class restaurant invents things, exceptional things (9)
ANOMALIES : A + NOMA(a Michelin star restaurant in Copenhagen) + LIES(invents things;tells untruths).
Defn: Things which deviate from the standard, normal or expected.
10 Proceed slowly and don’t start to take risks (5)
AMBLE : “gamble”(to take risks;to chance it) minus its 1st letter(don’t start …).
11 Snooping is certainly not flipping positive (5)
NOSEY : NO!(certainly not) + reversal of(flipping) YES(a positive;affirmative response).
12 Baseball player‘s pants and shirt? (9)
SHORTSTOP : SHORTS(underpants in North America, which are called pants in the UK) + TOP(a shirt, as is worn on upper half of the body).
Defn: … in the fielding team, positioned between second and third base.
13 He is too hammered to have the first bit of my drink (8)
SMOOTHIE : Anagram of(… hammered) HE IS TOO containing(to have) the 1st letter of(the first bit of) “my“.
Defn: … consisting of fresh fruit pureed with milk, yogurt or ice cream.
14 Nuts put back a couple of times (6)
TESTES : Reversal of(… back) SET(to put;to place) twice(a couple of times).
Answer: …, slang for which is “nuts”.
18 Tesla gets involved in German car manufacturer’s tests (6)
AUDITS : T(symbol for the Tesla, unit of magnetic flux density) contained in(gets involved in) AUDI(German car manufacturer)‘S.
20 Sci-fi film about small green animals (4,4)
STAR WARS : Reversal of(about)[ S(abbrev. for “small”) + RAW(green;inexperienced) + RATS(small but not green animals) ].
22 Fancy a drink immediately (4,1,4)
LIKE A SHOT : LIKE(to fancy;to desire) + A + SHOT(a small drink of spirits).
25 Part of a supermarket is covered in beer (5)
AISLE : IS contained in(covered in) ALE(a type of beer).
26 United supporters going round creating chaos (5)
SNAFU : Reversal of(… going round) [ U(abbrev. for “united”) + FANS(supporters of a particular person or thing) ].
Answer: …, acronym for “Situation Normal, All F***ed (or Fouled, even) Up”, in other words, a mess.
27 Being filthy is ultimately pointless when playing around with Tinder (9)
DIRTINESS : Anagram of(… when playing around …) [ IS + the last letter of(ultimately) “pointless” plus(with) TINDER].
28 Performers missing out on the two leading parts in Hair? (7)
TRESSES : “actresses”(female performers on stage or screen) minus(missing out on) its 1st two letters(the two leading parts).
29 Go mad, having binned your junk food (5)
DONUT : “do one’s nut”(to go mad;to get angry and agitated) minus(having binned) “one’s”(possessive pronoun for any person in general;your, as in “your;one’s understanding is appreciated”).
Down
1 What I’ve created here is an angry rumour (9)
CROSSWORD : CROSS(angry) + WORD(rumour;hearsay, as in “the word on the street is …”).
Defn: …, with “I” a self-referential pronoun for the setter.
2 Researcher‘s obsessive way assimilating something that’s unknown (7)
ANALYST : ANAL(obsessive;possessing and fixated on certain behavioural traits) + ST(abbrev. for “street”;way;thoroughfare) containing(assimilating) Y(symbol for a quantity that’s unknown).
3 Tight clothing hides middle of bum and ‘bits’ (8)
SKINSUIT : SKINS(hides of animals, especially when tanned or dressed) + the central letters, respectively, of(middle of) [ “bum” plus(and) “bits“].
Astronauts, too, wear them:
4 Grab stock from behind large, old boxes (5)
LASSO : ASS(one’s rear end;behind in North America, or “arse” in the UK) contained in(… boxes) [ L(abbrev. for “large”) ] + O(abbrev. for “old”) ].
Defn: To catch cattle with, well, a lasso.
5 The buttocks let out hot air (7)
PRATTLE : PRAT(again, a term for one’s rear end;buttocks) + anagram of(… out) LET.
Defn: Lengthy and foolish or inconsequential talk.
6 Go round the M25? Not with a learner! (5)
ORBIT : “orbital”(a ring road round, say, a city or other congested area, an example of which is the M25 around London) minus(Not with) [ A + L(plate displayed by a learner driver) ].
7 A legendary DJ’s spinning some R.E.M.? (5)
SLEEP : Reversal of(… spinning) [ PEEL(John, legendary disc jockey with BBC Radio 1)‘S ].
Defn: …, not the alternative-rock band, but the sleep phase characterised by Rapid Eye Movement, and dreaming.
8 Mineral revealed when a gas mine explodes (8)
MAGNESIA : Anagram of(… explodes) A GAS MINE.
Defn: … of magnesium oxide.
15 One shifted in a locomotive, transported only for a short time (9)
TRANSIENT : [ TRAIN(not a locomotive, but a series of carriages pushed or pulled by a self-propelled locomotive) + SENT(transported away) ] with “I”(Roman numeral for “one”) moved down(shifted, in a down clue).
16 Uncertainty shown by dodgy Trump acolyte on the radio (8)
SUSPENSE : SUS(short for “suspicious”;dodgy) + homophone of(… on the radio) Pence(Mike, USA Vice President, assistant;acolyte to Donald Trump).
17 Eminent old city said to provide housing (8)
STATURED : UR(Biblical city) contained in(… to provide housing) STATED(said;expressed in speech or writing).
19 Bowl-like containers and pots often smeared with sauce (7)
TEACUPS : Anagram of(… smeared …) [ the 1st and 3rd letters of(… often – a somewhat vague indicator if you didn’t already know the answer) “pots” plus(with) SAUCE ].
And surely the anagram indicator is misplaced in the midst of the fodder?
21 Extremely risqué setter gets rejected and principally needs to straighten up some more (7)
REALIGN : The 1st and last letters of(Extremely) “risqué” + reversal of(… gets rejected) GILA(this crossword setter) plus(and) the 1st letter of(principally) “needs“.
22 Zlatan’s debut in the roster … he scored (5)
LISZT : The 1st letter of(…’s debut) Zlatan contained in(in) LIST(a roster being a list of persons or groups).
Defn: … music.
23 Jack Kerouac’s novels are very entertaining at first (5)
KNAVE : The 1st letter of(… at first) “Kerouac’s novels are very entertaining“.
Defn: The Jack of any of the suits in a deck of playing cards.
24 He’s a criminal protecting the heart of Cardiff underworld (5)
HADES : Anagram of(… criminal) HE’S A containing(protecting) the central letter of(the heart of) “Cardiff“.
Great puzzle; lovely blog.
Had to think fairly hard about quite a bit of this, especially the Danish restaurant!
Some very funny gags in this puzzle
Yes, a pretty challenging Sunday offering. Had trouble with a few at the end and missed out on LAPDOGS. The restaurant referred to in ANOMALIES was an unknown and I hadn’t come across PRAT for ‘buttocks’. STATURED must be an uncommonly used adjective, but looking it up, it is in the usual places. I wouldn’t necessarily equate an ANALYST with a ‘researcher’; analysis can be research but not always.
I liked the ‘dodgy Trump acolyte’, TESTES and the surface for SKINSUIT which your picture shows is definitely not a good look!.
Thanks to Gila and scchua.
I would parse 29a simply as ‘do your nut’ minus ‘your’. Quite a few Americanisms not indicated, ‘ass’ in 4d and ‘donut’ as opposed to ‘doughnut’ to name a couple. Liked the sequence of ANAL, ASS, PRAT and, of course, the excellent clue for SKINSUIT. I suppose you could include HADES as a nether region. Other favourite clues include those for SNAFU and KNAVE. Thanks to Gila and scchua.