Continuity mistake: When Miles jumps off the ferry to swim ashore, the camera view is from the ferry: he jumps into quiet, fairly level water, yet the camera recedes from him (he jumped off the back of the boat as the camera continues moving with the boat). The angle changes and we see the wake of the boat - but it's not what he jumped into.
Other mistake: Laura is in the security control room of the plant, and finds a Master Lock Console screen; she sees it has Biometric Scan access and comments to Rich "It's not a retina scanner. It works on biometrics." She then brings up a photo ID of an employee on the monitor, lifts up the scanner and places it against the monitor, to get access. Firstly, retinal scans ARE biometric. She should have said "It's not an iris scanner," which requires a physical eyeball to scan. Secondly, no monitor from the 2005 period would be high-resolution enough to fool a biometric scanner. (00:25:20)
Character mistake: When Rich refers to the film showing Davis (decades ago), he figures they were in "Asia... Mongolia or somewhere." However, the film cannister had "Tibet, 1937" written on it - important enough to show the audience, but not for the character to read? (00:40:25)
Factual error: When Rich and Laura are checking the US Patent Office records for the Nortide drug, the date of the patent is shown as "December 22th, 1963." The form is a modern, barcoded typed document, not a hand-written or typed one, and supposedly a formal US government document, so the '22th' should not have happened. (00:15:45)