In Jigsaws lair, where he was caught, you can see items around the room from the house in which the 8 victims were being held. You can see the oar Amanda picks up from the basement and the X marks the spot photograph. These are clues to show that the camera footage is recorded. This is confirmed on the DVD commentary.
When Jigsaw and Eric escape the lair via a hidden elevator, the low-budget of the film prevented the construction of an actual working elevator. Thus, some tricky photography and editing was implemented. For the first shot where we see Jigsaw and Eric "going down", the scene was simply shot by raising the camera vertically to give the impression of them "going down" on an elevator. For the next wide shot, simple digital effects were added to make it appear that the room was "lowering." And for the final shot, where we see the top of the elevator going down an elevator shaft, stock footage from the film "Hollow Man" was used.
In the room with the razor blade box, if you look at the top of the frame, you can see a lock with a key in it. If the actress walked a few feet further, she could've unlocked the box and gotten the syringe. Obviously this would've defeated the purpose of her dying, but interesting to point out. Confirmed in DVD special features.