Mr. Burns collapses on a sundial pointing his arms at S and W - which to his eyes look like M and S - identifying the initials of the shooter. This resulted in several characters having their names permanently expanded solely for the sake of red herrings: Seymour Skinner's name was revealed as M. Seymour Skinner - this is written on a diploma behind his head in one scene - while Moe the Bartender became Moe Szyslak, and Sideshow Mel's real name was revealed as Melvin van Horn, presumably to eliminate him, though it could still have been interpreted as not MS, but SM, Sideshow Mel.
The budget proposals are: a crystal bucket and new blanket (Groundskeeper Willie), new kitchen staff (Lunchlady Doris), Tito Puente jazz class (Lisa Simpson), chocolate microscopes (Ralph Wiggum), double guitars (Otto) and more rubber stamps (Principal Skinner).
The biggest clue to the classic 'whodunit' - and the actual solution - is revealed at 7:46. When Mr Burns and Smithers are eating the chocolates sent by Homer, the first person to be revealed in the photograph underneath the chocolates is Maggie. The second is Santa's Little Helper, who was the other occupant of the car when Mr Burns was shot.