Mayhem By Vagans ( What Villainy!) http://www.crossword.org.uk/mayhem.html

[Matakari]

Good morning, there is a glimmer of hope for cracking
this one now. The last two DOWN and the only ACROSS.
Thanks in advance for your patience!

1(D) Clot of sticky stuff on highland river (6) : DO?SE?
34 (D) Girl's long-legged bird (3) : ?E?

38(A) Tea, bishop? We hear it's toast and salmon (5) : ?NA?R

( Villainy is afoot once again in an English village. Extra letters given by the wordplay of down clues (not to be entered) spell out a hint which can help identify the serial protagonist (and avoid two red herrings linked to the location). Solvers should highlight the name of the village (12) and the person responsible for the events (6) (17 cells in all). Chambers is recommended. )

[Neveracrossword]

1 Goosey (Goo+S(p)ey)

38 Charr - Cha+RR.

There must be more than a 'glimmer of hope' by now, surely?

[JJ109]

34 R(h)ea ?

[Matakari]

Many thanks, NAC, yes, the light is shining brighter now!
There seems to be a problem now with 34(D), jj109, the letters
left are: ?ER

34 (D) Girl's long-legged bird (3) : ?ER (HER )

[Paigntonian]

Long-legged bird = heron. That gives us the 'her' but can't parse it.

[Matakari]

Many thanks, Paigntonian, I saw it but just could not parse it either, or see any extra letter.

[ProfessorMaisie]

The alt spelling of heron is HER[n] so the 'n' is extra.

[Matakari]

Many thanks for this vital piece of information, ProfessorMaisie!