Most of the evidence in the game is required for advancement but the ones I noticed that weren't are:
Chapter 2: When to are following the trail of fluid when you get to the broken elevator investigate the top button on the elevator for a fingerprint.
Chapter 2: Before you move the locker (if you move it before checking the scratches you will have to redo the level) to get in the seceret room at the end of the level check the floor for scratches.
Chapter 4: Your lab lady mentions this but after the full blown hobo fight near the end of the level you have to photograph a map twice. First of the whole thing and then a close-up on the circled part.
Chapter 8: On the left wall of the hallway when you see the armless teacher bouncing around there is trace evidence on a stain of blood.