Two Birds of a Feather - S3-E19
Factual error: No matter how good of a pilot Samuel is, he's chasing a Learjet 24 plane with a WWII design P-51 Mustang (that he does not even know how to start, but of course fictional pilots can just 'wing it' and do amazingly). Assuming that speed is not a factor since the bad guy is not flying at top speed just yet (but still he has a projected arrival time of 6 hours, meaning he'd fly around 700 kmh), they do the chase at high altitude (42,000 feet are mentioned), with Samuel not wearing a mask or anything in a non-pressurized plane! He'd have passed out.
Factual error: When Blackthorne is on Rodrigues' ship, Rodrigues offers him grog. But grog was only invented in 1740, by British Vice Admiral Edward Vernon, whose nickname was "Old Grog" because of his preference for coats made of grogram cloth.