Wait For It... solution
by Kegler

As shown by the highlighted squares, the letters in the phrase THE OTHER SHOE “drop” to the bottom of their respective words.

Wait For It...  solution grid

Across
1SEE + P
4SIGHTS ("SITES" hom)
10PI(PI)TS
12L(AG)OON
13AGENdA
14TIM (rev)
15CUR + L
16CH + A + T
17SU + TRA (rev)
18HO(LIE)ST
19R(HYMn)EaRS
21TI(L)DE
22BLEAT (TABLE anag)
24C(LI)ENTS
29TREACLE (ELECTRA anag)
32S + CATS
34OSLO (SOLO anag)
35E + IRE
36PR + O
37L(EVE) + L
38SESTET (TSETSE anag)
39RESIDE (DESIRE anag)
40ET(C)HER
41monSOON
Down
1SPACER (rev)
2[H/w]EIGHT {"drop" the H}
3P(O)INT {"drop" the O}
4STARTLE (RATTLES anag) {"drop" the T}
5GE + LID (EG rev) {"drop" the E}
6H + AMS
7SHO(U)T {"drop" the H}
8TOR + RID
9UNLEAD (hidden) {"drop" the E}
11STA(I)R
15CUT + I + E
20MATTEr
21TRICK + LE {"drop" the R}
22BA(S)TES {"drop" the T}
23LACIER (ECLAIR anag)
25LAB + OR
26TOO + LED {"drop" the O}
27STOL + EN (rev)
28PEARS ("PARES" hom) {"drop" the E}
30HEAR + T {"drop" the H}
31SLOpES {"drop" the S}
33SPECials