Towards the end, Jake is exuding blood from both sides of his mouth when Warner inserts the tube into his lung. When Danny apologizes, blood is only shown on his left side of his mouth and the flow of blood is not present on the right. No staining or evidence is there outside of the initial spurts when he coughed it up.
While it's true that many printers do place their Machine Identification Code in microscopic dots on the printed page, there's no way that they could have helped solve this case because the dots are too small to be picked up and transmitted by the sending fax machine.
Dr. Warner says that as an Air Force doctor, she did two tours at Ramstein Air Force Base. But she pronounces it "Rahm-steen," a mistake no veteran would ever make.