Intersections solution
by Kegler

The extra letters (highlighted in their clue words below) spell EVEN ROWS, EVEN COLUMNS; these squares are shown in the grid in blue.
When read left to right and top to bottom, they spell HOPPING, SKIPPING AND JUMPING.

Intersections solution grid

Across
4LOSE (SOLE anag) [Wine]
7S(W)AT
11SHOOT ("CHUTE" hom) [curve]
12P(O)I
13TON + N + EAU (NOT rev) [CARE]
14RDA (hidden) [neater]
16SIKKIM ("SIC 'EM" hom) [Indira]
17RE + RUN (URN anag)
18D(E)ANE
21O + PTIONS (POINTS anag)
23OL + LIE (LO rev) [alloy]
25N(Y)ALA (ALAN rev)
28yEARNED
30TSO (SOT anag)
31AMBIENT (BAN ITEM anag) [wall]
32M(O)P [stool]
33S + NAGS [heard]
34Y + AMS
35STUN (NUTS rev) [revel]
Down
1A(ST.)IR
2SHO(N)E [died]
3CONTROL ROOM (MR. COOL OR NOT nag)
4LONG (hidden)
5SPAS + M [throne]
6EMU (hidden)
7SPOKE + N [coral]
8WOR + KAS(A)T + EAM (rev)
9A + ID + IN + G [Founding]
10T(H)AMES
15AN + T + E [belt]
18DOnNE [rued]
19POE + TRY
20PLASM + A (PALMS anag)
22P(IN)UPS
24AD(M)IT [Mallow]
26LU(N)GE [Nat]
27ANTSY (TANSY anag) [sedge]
29J + INN
31ADS (SAD anag)