Thank you to Xestobium. Definitions are underlined in the clues.
Across
1 Primate has company with devilment? (6,8)
MONKEY BUSINESS : MONKEY(a small to medium-sized primate) plus(has) BUSINESS(a company/a commercial organisation).
Defn: …/reckless mischief.
9 Being left-handed, I slant, sir, all over the place (9)
SINISTRAL : Anagram of(…, all over the place) I SLANT, SIR.
10 Guy providing drinks for the audience? (5)
TEASE : Homophone of(… for the audience) “teas”(drinks).
11 Get backing part in ELO recording (4)
ROLE : Hidden in(Get backing) reversal of(part in) “ELO recording”.
12 Hundreds once obeyed their orders (10)
CENTURIONS : Cryptic defn: Leaders of centuries, companies in the ancient Roman army, originally of a hundred men each.
14 Eatery as top grub organisation? (9)
GASTROPUB : Anagram of(… organisation) AS TOP GRUB.
16 The Spanish leading European reform initially – one that’s completely unsuccessful (5)
LOSER : LOS(Spanish for the article, “the”) plus(leading) 1st letters, respectively, of(.. initially) “European reform”.
17 Invert bobbin to produce twists (5)
LOOPS : Reversal of(Invert) “spool”(bobbin/a cylindrical device round which thread is wound in weaving or sewing machines).
19 Need crate rebuilt so this can be staged again (2-7)
RE-ENACTED : Anagram of(… rebuilt) NEED CRATE.
21 Confection that may be an alternative to Bath bun? (6,4)
SPONGE CAKE : SPONGE(to cleanse with a sponge/an alternative to “to bath”/to cleanse by immersion in a bath) + CAKE(an example of which/? is a “bun”, a small cake usually containing dried fruit).
23 Either way, it’s a mistake (4)
BOOB : A palindromic word(Either way) for a “mistake”.
26 Pole getting in point about particular view (3-2)
END-ON : N(abbrev. for the north pole) contained in(getting in) reversal of (… about) NODE(a point where lines, in say, a diagram, intersect).
Defn: …, one with the tip of an object facing the viewer.
27 He’s a louse, getting drunk in such places (9)
ALEHOUSES : Anagram of(…, getting drunk) HE’S A LOUSE.
28 Would one go into the theatre with such a person, to get a better look? (7,7)
PLASTIC SURGEOENS : Cryptic defn: Reference to an operating theatre where a patient may have cosmetic surgery to look better.
Down
1 Degrees presented, with some hesitation, for microwave device (5)
MASER : Plural of MA(abbrev. for Master of Arts, a graduate degree) plus(with) ER(an expression of some hesitation/uncertainty).
Defn: Acronym for a microwave device, viz. one that provides “microwave amplification by the stimulated emission of radiation”.
2 Make uncertain? It just doesn’t add up (7)
NONPLUS : NON(prefix indicating “not causing”/just does not) + PLUS(to add up two or more quantities).
Defn: To confuse, hence ….
3 Teaset encapsulates peace and quiet (4)
EASE : Hidden in(… encapsulates) “Teaset”.
4 Member of pub staff to prohibit entry to footballer? (9)
BARKEEPER : BAR(to prohibit/prevent entry) + KEEPER(short for “goalkeeper”, a member of a football team).
5 The sound of something squishy striking part of chair, possibly (5)
SPLAT : Double defn: 1st: … a surface with force; and 2nd: A piece of thin wood, possibly as part of a chair back.
6 AA rung last: desperate to obtain fuel (7,3)
NATURAL GAS : Anagram of(…: desperate) AA RUNG LAST.
7 Salts, one might say? (7)
SEASONS : [SEA SONS](or “sons of the sea”, as one might call sailors/salts).
Defn: Adds salt to food.
8 Mining Engineer guaranteed to lose spades – it could be deliberate (8)
MEASURED : ME(abbrev. for “mining engineer”) + “assured”(guaranteed/made sure that something will happen) minus(to lose) “s”(abbrev. for “spades”, a suit in a deck of cards).
13 Those who once provided ships’ crews: groups of hacks? (5,5)
PRESS GANGS : [PRESS GANGS](how one might describe groups/crowds of hacks/members of the press).
Defn: … by enlisting men forcibly.
14 Woman getting shoes ordered: such things will keep your feet dry! (8)
GALOSHES : GAL(informal term for a “woman”/girl) plus(getting) anagram of(… ordered) SHOES.
Defn: … and your shoes dry too.

15 Such tiny joints are said to be the best! (4,5)
BEE’S KNEES : Literally/said to be, the joints in these particular tiny insects, corresponding to the joints in human legs.
18 Loo diva redesigned in special shape (7)
OVOIDAL : Anagram of(… redesigned) LOO DIVA. Another anagram, “OVALOID” has the same meaning, coincidentally!
20 Ties top of overshoe to upset child’s foot (7)
TOOTSIE : Anagram of(… upset) [TIES + 1st letter of(top of, in a down clue) “overshoe” + TO].
Defn: A child’s word for “foot”.
22 Garment one furry creature provided (5)
COATI : COAT(an outer garment) + I(Roman numeral for “one”).
24 Sexually experimental offspring is an animal (5)
BISON : BI(short for bisexual/sexually attracted to more than one sex – though I’m not sure that “experimental” is an appropriate description) + SON(a male offspring).
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25 Type of screen raised to provide means of entry (4)
DOOR : Reversal of(… raised, in a down clue) ROOD(a type of screen/partition between the chancel and the main part of the church).
Another enjoyable puzzle from Xestobium and thank goodness the site started running again in time to applaud his efforts.
Top three here were BEES KNEES, SPONGE CAKE & MONKEY BUSINESS.
Many thanks to Xestobium for the fun and to scchua for waiting patiently to post the review.
Thanks, Xestobium and scchua!
Enjoyed the puzzle and the blog (in addition to being detailed, it is pleasant to the eyes!).
OVOIDAL
Should the definition be ‘in special shape’?
KVa, right. Blog corrected.