Factual error: At the very start, the lead parachutist says they're jumping from 30,000 feet, the altimeter confirms it, everyone whoops and cheers, and he gets them to put their masks on just before jumping. Two problems - the plane they're in is a De Havilland DHC-6 Twin Otter with a maximum altitude of 25,000 feet. And at 30,000 feet in an unpressurised aircraft there'd be nowhere near enough oxygen for shouting and cheering - they all should have had their masks on already.
Factual error: Delores strikes a match and there is a huge explosion like a fuel-air weapon. The room has been filled with more than the usual amount of oxygen, but oxygen does not burn by itself; it combines with fuel, and that is the fire. The match would burn much more intensely and quickly because of the extra oxygen, but the only fuel would be the match, the cigarette, and perhaps the rest of the box of matches, which would only make a small fire.
Episode #1.6 - S1-E6
Factual error: In Episode 6, Vincent comes out of his apartment building and before he reaches the curb, and has a chance to hail a cab, one is waiting for him. There was no ability to book a yellow cab in the 1980s.
And in the Beginning... - S1-E1
Factual error: The show is set in 1991, and Dexter walks past a Lehman Brothers stall at the jobs fair. The problem is that the stall and the marketing materials on it have the modern-day Lehman Brothers logo and branding. Back in 1991, the bank was called Shearson Lehman Brothers and had a completely different logo and colour scheme. It was only spun off into Lehman Brothers in 1994. (00:10:03)