Cryptic crossword - letters latent

Question

"Whose idea was it to say that we'd answer every complaint we received?" Svetlana was sat at Coldport City Council's Complaints desk staring at a sheet of paper. Bob, her colleague, looked up. "The Mayor's, I think," he said. "What's the problem?" Sveta passed him the paper. "Apparently," she said, "we have to solve the crossword to determine the complaint. All I know is what's on that paper, and that it's a complaint about that new Bulgarian restaurant."

This is a cryptic crossword with letters latent: all the clues contain an extra letter that must be removed before solving. Removing the letters leaves real words. The extra letters spell out a (slightly ungrammatical) phrase that should help solvers determine the complaint that is being made. To further help solvers, it is recommended that blue shaded cells are filled with lower-case letters and all other cells use upper-case letters. All but one entry may be found in Chambers Dictionary, and one entry is an abbreviation. Solvers should show the completed crossword, the hidden phrase, and explain what the complaint being made is.

NOTE: 20down is not letters latent because I missed it out in the clueing list and putting it back in properly would alter a significant number of clues around it.

Across
1.  Japanese flight?  Add nothing (4)
5.  Scrutinizes lava casually in schistous coat (5)
9.  Regular party hats historical cost (4)
10. Slavonic accent, one I found in Hong Kong unofficially (5)
12. None, accordingly, equal as combining form (3)
13. Spoil roman areas -- cut short (3)
14. Spacewalk, perhaps unbelievably, restrains nit (3)
15. They dare heads of criminally active patriarchal institutions (4)
16. Clack of pulse? It's... knotty (5)
17. Choosey; exclusive but not special (5)
19. Foretell carse losing special factor to Germany (4)
21. Scottish grate, brittle when bit of chair is burned (5)
23. You'll regularly trim Hansl magnolia (5)
25. Tattered tunic set in spaces left in the worlds (5)
27. Work laboriously: it ends up you'll go, maid! (4)
29. Draco's letter to Goddess of crash-action is laid-back (3)
30. Praetorian hill displays Liverpool terracing (3)
31. Talking beginnings of a highly ambitious Norwegian collective (1-2)
32. Pill-treated wines strengthen poetically (5)
33. Exalt Morocco's islamic ruler: "Leaders' leader" is hexact (4)
34. Twelve months anew makes Will mourn (5)
35. Greek character's flightless bird clutching bone qubits from river (4)

Down
1. Dude, ice spires are repositories of cumin and turmeric! (9)
2. Taurus (not Tut!) arranged 'major' part of two constellations (4)
3. No powers in masculine agreement for the short-sighted (6)
4. Chore of nose (sensitive instrument): amplifier of noise and relating to smells (5)
5. Ramshackle housing set forth about asocial insect from Yukon Territory (10)
6. St. John's bread is returned in arboraceous cran (5)
7. 8's mane was on top, served without reply (4)
8. Holt state confidentiality agreement covers 14 (6)
11. Ask Leander nicely for lists of prisoners awaiting trial (9)
18. Scottish finch scraped linen that is to stay (6)
20. Irish sage is reformed mollah (6)
22. Once ant emetic starts to provoke uprising, kill esophageal reflex (5)
24. Meal, note, complete without stimulant (5)
26. John got half at Brest, known for where water became wine (4)
28. States nothing twice, concealing greeting (4)

[Any feedback on the clues is welcomed as well; generally I think the clues make more sense without the added letters as I think that's the most reasonable thing for the solvers.]

Answer 1

Grid:

Letters latent and super-brief wordplay explanations:

Across
L 1.  Japanese f[l]ight?  Add nothing (4) [SUM+O]
A 5.  Scrutinizes lav[a] casually in schistous coat (5) [CAN in SS]
T 9.  Regular party ha[t]s historical cost (4) [PaRtY + 's]
I 10. Slavonic accent, one [I] found in Hong Kong unofficially (5) [ACE in HK]
N 12. [N]one, accordingly, equal as combining form (3) [I+SO]
A 13. Spoil roman are[a]s -- cut short (3) [MARs]
N 14. Spacewalk, perhaps unbelievably, restrains [n]it (3) [substring]
D 15. They [d]are heads of criminally active patriarchal institutions (4) [&lit]
C 16. [C]lack of pulse? It's... knotty (5) [NO DAL]
Y 17. Choose[y]; exclusive but not special (5) [sELECT]
R 19. Foretell ca[r]se losing special factor to Germany (4) [BOX with X -> DE]
I 21. Scottish grate, brittle when bit of cha[i]r is burned (5) [CRISP minus C]
L 23. You'll regularly trim Hans[l] magnolia (5) [YoUlL + hANs]
L 25. Tattered tunic set in spaces left in the wor[l]ds (5) [anag]
I 27. Work laboriously: it ends up you'll go, ma[i]d! (4) [last letters; could remove A instead]
C 29. Draco's letter to Goddess of [c]rash-action is laid-back (3) [ATE<]
A 30. Pr[a]etorian hill displays Liverpool terracing (3) [double def]
L 31. Ta[l]king beginnings of a highly ambitious Norwegian collective (1-2) [initial letters]
P 32. [P]ill-treated wines strengthen poetically (5) [anag]
H 33. Exalt Morocco's islamic ruler: "Leaders' leader" is [h]exact (4) [OP explains: initial letters; "leader is exact" seems a bit of an odd def to me]
A 34. Twelve months [a]new makes Will mourn (5) [YEAR+N; Will Shakespeare]
B 35. Greek character's flightless bird clutching bone qu[b]its from river (4) [OP explains: RHEA clutching OS minus EA, but isn't "quits from" the wrong way around then?]

Down
E 1. Dud[e], ice spires are repositories of cumin and turmeric! (9) [anag.]
T 2. Taurus (not [T]ut!) arranged 'major' part of two constellations (4) [anag after removal]
S 3. No power[s] in masculine agreement for the short-sighted (6) [OP in M YES]
H 4. C[h]ore of nose (sensitive instrument): amplifier of noise and relating to smells (5) [nOSe+MIC]
A 5. Ramshackle housing set forth about asocial insect from Yukon Territory (10)
R 6. St. John's bread is returned in arboraceous c[r]an (5) [rev substring]
E 7. 8's mane was on top, served without reply (4)
L 8. Ho[l]t state confidentiality agreement covers 14 (6) [NDA covers EVA]
E 11. Ask L[e]ander nicely for lists of prisoners awaiting trial (9) [anag]
T 18. Scottish finch scraped linen that is to s[t]ay (6) [LINT + i.e.]
- 20. Irish sage is reformed mollah (6) [anag]
T 22. Once an[t] emetic starts to provoke uprising, kill esophageal reflex (5) [initial letters]
E 24. Meal, not[e], complete without stimulant (5) [(-s)UPPER but can't quite parse]
R 26. John got half at B[r]est, known for where water became wine (4) [CAN+A(-t), "best known"]
S 28. State[s] nothing twice, concealing greeting (4) [HI in OO]

I'm still thinking about the wordplay for 33a and 35a, though I have all their letters. I'm not sure I quite grasp the parsing of 24d.

Now

we should, as per the remark that LATIN AND CYRILLIC ALPHABETS SHARE LETTERS, interpret the shaded letters as Cyrillic, which is why some needed to be lowercase. This seems to yield something like У НАС ЕСТЬ ТАКО РАН which Google Translate tells me translates from Bulgarian to English as WE HAVE SO EARLY. The OP kindly informs me in comments that there's a minor error, the К and Р being transposed ... and У НАС ЕСТЬ ТАРОКАН apparently translates as WE HAVE A COCKROACH. Ugh!