In the scene when the fake Sydney extracts the second half of the computer chip from Vaughn's chest in Nepal, we see Sydney digging around with tongs under his skin, find the chip, and slowly draw it from the wound to show the audience. We then see blood across the top of the chip but none on the bottom when Sydney turns it over and none on the tongs themselves.
Also, Vaughn claimed not to know the chip was in his body for the last 30+ years. With as many times as we've seen him injured and hospitalized over the course of the show, how would repeated body scans, MRI's, x-rays, etc. miss a foreign object planted so close to the skin's surface in such an accessible part of the body?