The theme is provided by 36-Across: Incompatible. Answer: Like oil and water. The fills for “oil” and “water” are a rebus, each word appearing three times, “oil” in the upper section of the grid, “water” in the lower section. Both words appear in 31-Down, thereby negated the concept that oil and water do not mix.
20A. Food wrap = Tin f[oil]/4D. Jumps back = Rec[oil]l
22A. Light for Aladdin = [Oil] lamp/10D. Cry at an unveiling = Et, V[oil]a
34A. Chicken for dinner = Br[oil]er/31D. Lightly scented perfume = T[oil]et [water]
43A. Soother of an aching joint – Hot [water] bag/31D. Lightly scented perfume = T[oil]et [water]
62A. Brine = Sea [water]/50D. Restaurant freebie = Ice [water]
64A. Wakeboard relative = [Water] ski/ 52D. Idea condition in which to ford a stream = Low [water]
There are also 10 single letter circle fills: L,K,T,O,L,W,T,T,M,R. I haven’t a clue what they mean.
Another interesting aspect of this puzzle is that eight down fills have two clues whose answers are unrelated to each other.
1D. _____America/Final maneuver = Captain/Last pass
2D. It gives Congress the power to declare war/Cyclist’s stunt – Article 1/Wheelie
3D. Séance phenomena/Seattle Center Coliseum, since 1995 = Trances/Key Arena
11D. Fruit or nuts/Silhouette = Bananas/Outlines
12D. Fourth pope/Snitch = Clement I/Rat fink
13D. Crimson/Opera texts = Deep red/Libretti
25D. Big band member/Wee one = Tuba/Toddler
28D. _____avis/Two- or four-seater, maybe = Rara/Maitre D’