Thanks to Hectence for this nice Quiptic. Definitions are underlined in the clues.
It’s a “pangram”: A to Y plus OMEGA, the last in a series, or Z in this case.
Across
1 Select the French relish (6)
PICKLE : PICK(to select out of many) + LE(French for the article, “the”).
4 Lady’s half cut after quite strange drink (7)
TEQUILA : “Lady” minus its last 2 letters(…’s half cut) placed after(after) anagram of(… strange) QUITE.
9 Examine said rule first to get ticket that’s valid later (4,5)
RAIN CHECK : CHECK(to examine/to vet) placed after(… first) homophone of(said) “reign”(to rule).
10 Animal taking over English river’s eating tons (5)
OTTER : [O(abbrev. for “over” in cricket scores) + E(abbrev. for English) + R(abbrev. for “river”)] containing(…’s eating) T,T(twice/…s abbrev. for “ton”, a unit of weight).
11 Urge politician to block stupid lie (5)
IMPEL : MP(abbrev. for a Member of Parliament, a politician) contained in(to block) anagram of(stupid) LIE.
12 Often Mum’s describing an unknown era (4,1,4)
MANY A TIME : MA(Mum/one’s mother) containing(describing) [AN + Y(symbol for an unknown quantity in algebra)] + TIME(a period of which “era” is an example).
13 Bird comes down shortly before light (7)
LANTERN : TERN(a seabird) placed after(… before) “lands”(comes and touches down after a flight) minus its last 2 letter(shortly).
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15 Idiot returned money with reduction (6)
NITWIT : Reversal of(returned) TIN(slang for “money”) + “with” minus its last letter(reduction).
17 Delighted with a thought (6)
AMUSED : A + MUSED(thought/contemplated).
19 North American scientific establishment rejected church correspondence (7)
BALANCE : Reversal of(… rejected) [NA(abbrev. for North American) + LAB(short for “laboratory”/an establishment for scientific testing and experimenting)] + CE(abbrev. for the Church of England).
Defn: The condition of different elements in a situation being equivalent/corresponding to each other. 
22 Grouses about window finally breaking, putting a thousand on estimate (9)
GUESSWORK : Anagram of(… about) GROUSES containing(… breaking) last letter of(… finally) “window” plus(putting a … on) K(abbrev. for “thousand”, informally).
24 Home game includes last in a series (5)
OMEGA : Hidden in(… includes) “Home game“.
26 Seaman’s forbidden in the vicinity (5)
ABOUT : AB(abbrev. for “able-bodied seaman”) + OUT(forbidden/not acceptable).
27 Most intelligent rodent without hesitation in desert (9)
SHREWDEST : SHREW(a rodent resembling a mouse) + “desert ” minus(without … in …) “er”(an expression of hesitation).
28 Tortured senator for disloyalty (7)
TREASON : Anagram of(Tortured) SENATOR.
29 Producer of milk with thick top (6)
JERSEY : Double defn.
Defn. 1 in defn. 2:

Down
1 Catch up with 1 across left incomplete (7)
PARTIAL : Reversal of(… up, in a down clue) TRAP(to catch/capture with, well, a trap) plus(with) IA(abbrev. for “1 across”, as used for crossword clues, with the Roman numeral substitution for “one”) + L(abbrev. for “left”). 
2 Tweet about redhead with cool clothing (5)
CHIRP : C(abbrev. for “circa”/about, in reference to specific years or time periods) + [1st letter of(… head) “red” contained in(with … clothing) HIP(cool/with it/very fashionable)].
3 We call son about things happening near home (5,4)
LOCAL NEWS : Anagram of(… about) WE CALL SON.
4 High grade knowledge crammed in can be absorbed (5,2)
TAKEN IN : [A(a high grade, as with grading students’ test papers) + KEN(one’s range of knowledge and understanding)] contained in(in) TIN(a metal can).
5 Share question on team regularly (5)
QUOTA : QU(abbrev. for “question”) + 1st, 3rd and 5th letters of(… regularly) “on team“.
6 Feeling for Greenlander with temperature inside home about zero (9)
INTUITION : [INUIT(one of the indigenous people of parts of Greenland) containing(with … inside) T(abbrev. for “temperature” in physics)] + [IN(at home/not out) containing(about) O(letter representing 0/zero)].
7 Allowed one good journalist to follow soldiers (6)
AGREED : A(article for “one”/a single) + G(abbrev. for “good”) + [ED(abbrev. for “editor”, a journalist) placed below(to follow, in a down clue) RE(abbrev. for the Royal Engineers, soldiers in the British Army).
Defn: Accepted by all parties and therefore allowed.
8 Rats maybe found inside? Never mind! (6)
VERMIN : Hidden in(found inside?) “Never mind“.
Defn: Of which rats are an example/maybe. 
14 Chart-topping song has Eno making a comeback (6,3)
NUMBER ONE : Reversal of(… making a comeback) Eno, or the number 1.
Defn: … on the hit parade.
16 Sad story reported dog and old women seized by enemy (4,2,3)
TALE OF WOE : Homophone of(reported) “tail”(to dog/to follow) + O(abbrev. for “old”) + [W(abbrev. for “women”) contained in(seized by) FOE(the enemy)].
18 Decline evil calls (5,2)
DROPS IN : DROP(to decline/to decrease in quality or quantity) + SIN(an evil/an offence).
Defn: … on/visits.
19 King and Queen welcomed in niche bread shop (6)
BAKERY : [K(abbrev. for “king”, in chess notation) plus(and) ER(abbrev. for Elizabeth Regina, Queen Elizabeth)] contained in(welcomed in) BAY(a niche/a recess formed by, well, a bay window).

20 Absolutely demand extremes of loyalty (7)
EXACTLY : EXACT(to demand and obtain something from someone, as in “to exact payment from …”) + 1st and last letters of(extremes of) “loyalty“.
Defn: Used to express absolute agreement to what has been said.
21 Heading off and travelling #amazed (6)
AGHAST : 1st letter of(Heading) deleted from(off) and anagram of(travelling) “hashtag”(represented by the symbol #).
23 Locates reported tourist attractions (5)
SITES : Homophone of(reported) “sights”(tourist attractions).
25 Equal odds in final game against English partners (5)
EVENS : Last letter of(final) “game” + V(abbrev. for “versus”/against, as in the Lions v. the All Blacks) + E(abbrev. for English) + N-S(abbrev. for “north” and “south” respectively, terms for the 2 players partnering against E-W in bridge, the card game).
Thanks Hectence and scchua
Very nice. Favourites were PARTIAL for the misleading 1a, VERMIN and BAKERY.
Hectence perhaps missed a trick with OTTER, as it’s also the name of a river in Devon, home to beavers!
Pretty good on the whole. I think it must take skill for a setter to make all clues of a similar level of difficulty, which was the case here, at least for me. One quibble in 27a: a shrew may somewhat resemble a mouse but it is not a rodent, it’s what was once called an insectivore (now classified in order Eulipotyphla).
Thanks scchua and Hectence.
Thank you both for this. In 14d I read the definition as “chart topping”; then “song” as NUMBER and ONE as the reversal of “Emo”.
Me @2: wikipedia article about shrews.
I mean “Eno” of course…
Yes, I took ONE as a reversal of (Brian) ENO, ex Roxy Music, and proponent of “ambient music”.
The real revelation for me was the true meaning of “raincheck”, in which I’d always assumed people were saying they’d “check” (as in restrain) their plans because of the rain. But no, thanks to Hectence (and Chambers) I now know that the “check” refers to a ticket that you take because the event you’re at has been rained off (probably baseball, given the US origins).
Thanks to Hectence for a smooth and easy solve, although with a couple of clues that were a bit tricky for a Quiptic. I parsed NUMBER ONE as did beobachterin and muffin, but I like scchua’s parsing better. Thanks also to scchua for the picture of the Jerseys in their jerseys.
This was a satisfying solve. AGHAST was a guess which I couldn’t even begin to parse, so thanks to Scchua for the explanation (and for the rest of the blog – especially the pic of jerseys in jerseys!). I had been thinking it was unlike the brilliant Hectence to get two letters away from a pangram and then not complete it, and Scchua’s pointing out that Omega gives us the “end” covers the Z, clearly; however – and this may just be me being dim – what about the F??
Anyway, thank you both Hectence and Scchua for a fun morning.
Weelbeck @9, there is an F in 16d. I had noticed the near-pangram and forgot to compliment scchua on spotting the “hidden” Z.
Wellbeck @9
tale oF woe
Oh I’ve just spotted it: “tale oF woe”. I KNEW it had to be me being dim!!
I’ll get my coat…
Thanks Muffin and DaveInNC: we crossed!
Interesting comment Wellbeck @9. It’s the old brain exercise: how many times does the letter f appear in the following sentence…
“Finished files are the result of years of scientific study combined with the experience of years”
Our brains are not particularly good at spotting the f at the end of the word “of”, possibly because we don’t pronounce it as v. Many many people give an answer of 3 or 4 to the above question.
* or even because we DO pronounce it as v!
I thought this was tougher than the cryptic but it might just be my addled brain.
Overall, a good crossword, although I don’t think ‘shortly’ should be used to indicate a double deletion, especially in a puzzle for beginners.
I thought that VERMIN was cleverly hidden, and I imagined the hashtag was just a Grauniad typo, doh!
Thanks Hectence and scchua.
Thanks, beaulieu, you got in first. We’re back to Deer v Antelopes. A shrew, whether in old classification or new is not, and has never been, a rodent. Enjoyed this, but agree the Cryptic was easier. Again.
Surely # is a hash symbol. The text that follows, e.g. pedant in #pedant is a tag. The two together are the hashtag. I realise some people do call # a hashtag, but they are wrong to do so, aren’t they?
The standard way to to read it would be to say ‘hashtag amazed’. This isn’t some people, it is the widly accepted way to read it. If someone said ‘hash amazed’ it would sound incorrect (to me at least). I think you have to accept that punctuation marks get new names when they are used in new ways.