Revealing mistake: When Dean cuts leviathan-Dean's head off, if you look closely you can see that a) the decapitated head disappears while it is still in the air, and b) when the body recoils, its hands disappear.
Continuity mistake: Elliot Ness and Dean are in his car waiting for the god of time. Elliot takes out his flask, takes a drink, offers some to Dean. Dean declines and Elliot puts the flask back in his pocket. The next shot Elliot is taking a drink again without pulling it back out of his pocket. (00:35:00)
Plot hole: In episodes where Sam and Dean are required to perform spells/rituals at certain times, the issue not quite seen is that not all clocks are exactly in sync with each other, meaning that the clock they are using could be off by a few minutes especially if dealing with different time zones or time periods. (S07E12, Time After Time).
Answer: Angels themselves may not have genitalia, but their vessels do. Nephilim occur when an angel in a vessel reproduces.
Greg Dwyer