The title of the puzzle is a combined reference two aspects of the game Clue. First, it alluded to "the usual suspects," the term used to refer to Col. Mustard, Prof. Plum, Mr. Green, Mrs. Peacock, Miss Scarlet, and Mrs. White in the opening scene. Second, the "pieces" are the game pieces from the board game Clue, which had the exact same colors as the colored shapes.
This was a hint to the teams to think about colors of the shapes and the characters they referred to. Teams needed to notice that each color had exactly the same number of shapes as the suspect of that color had letters. The shapes therefore constituted a substitution cipher for letters.
Looking, for example, at the red shapes, one could figure out which letters each shape substituted for. The parallelogram appears in Mustard and Scarlet, so it must be an S. The semicircle appears in Peacock and Scarlet, so it must be C. The square appears in Mustard, Peacock, and Scarlet, so it must be an A. And so on.
This gave the following cipher:
A = square
C = semicircle
D = equilateral triangle
E = circle
G = pentagon
H = plus sign
I = shield
K = right triangle
L = crescent
M = arrow
N = 5 pointed star
O = heart
P = hexagon
R = rectangle
S = parallelogram
T = kite
U = trapezoid
W = octagon
In this manner, teams could crack most of the cipher. However, a few shapes remained indeterminate and must be interpreted from context. That context was the message in the gray shapes in Part II. Given what can be determined from the colored shapes, the gray shapes give:
M/U
H/I/W
S
S
H/I/W
K/O
G/N
S
A
G/N
T
A
C
L
A
R
A
If the "Clara" at the end wasn't enough finish the message, then appeals to arguments about which letters must be vowels or just working through the possibilities yields:
MISSIONSANTACLARA
or Mission Santa Clara.
