Visible crew/equipment: Teddy, Leonard and Jimmy leave Jimmy's motel room and Leonard tells Teddy, "Take your own car." In the next shot as Teddy reaches for his door, a crew member, plus another one under his arm/elbow, are very clearly visible in the door mirror. Then as Teddy closes the door a crew member's face is seen on the left, in that mirror. (00:44:00)
Visible crew/equipment: As Leonard stands in the bathroom looking at Dodd, unconscious on the floor after the two fought, visible in the reflection of the mirror behind him is a dark haired crew member with a blue shirt. It's in the same shot as the housekeeping woman that knocks. (00:47:15)
Visible crew/equipment: When Dodd pulls in behind Leonard in the alley the crew is reflected in his SUV. (00:53:00)
Answer: It is never explicitly given. The most Leonard says on the subject is: "I'd rather be mistaken for a dead guy than a killer." Speculations include (you can make up your own motives as well) : (1) The clothes and car are so much nicer than his. If you are willing to kill someone: stealing is not really a "crime." Why not take the nicer objects? (2) It could be part of his "routine": Kill a man, take his clothes and car. The clothes he had on and the truck may be from the man he killed a year ago. (3) It could be that he wants to make the killer of his wife suffer even more, and takes his clothes as a way of humiliating him. Leonard takes the man's life-his clothes and car, which are wrapped up in his identity-just as the man took his. This idea seems to work with a theme in Memento about "Identity" (especially mistaken identity). Natalie thinks Leonard is Jimmy, then thinks he is Teddy, then learns he is Leonard. Teddy is "mistaken" for the second killer, Jimmy is "mistaken" for the 2nd killer. Sammy's story as a part of Leonard's story, etc. (4) It could "simply" be explained as a "plot device": Leonard has to do it, otherwise he won't find the note in "his pocket" and meet Natalie. (5) Leonard doesn't want to admit he's a murderer. He's lying to himself. If he's the victim, then he cannot be the murderer. (6) Leonard takes Jimmy's clothing as part of his routine of killing J.G.'s he becomes another person, he's the victim not the killer, thus "I'd rather be mistaken for a dead guy than a killer." and that's why he also takes his car, so he has to, once again, find his wife's killer and kill him.