anyone know the origin of the phrase "screwed up"?

If I may…

When you are screwing two items together the screw needs to go down so it can bite into both items.

If you are turning the screw up it is not bringing the two items into contact.

Thus you are doing it wrong

That’s pretty much what my question was from the beginning–I know what ‘screwed up’ actually means, and I’m familiar with the use of ‘screw’ for intercourse, but what I’m trying to get at is if there is any legitimate reason to assume that the ‘screw’ in ‘screwed up’ is actually related to the sexual term.

You may, but you would be providing what is know in linguistic circles as a folk etymology: an invented etymology that appears to make sense, but which does not actually conform to the historical chain of events that led to the use and meaning of the word or expression.

Based on its rise to prevalence during WWII, (regardless what other coincidental uses may have preceded it), and the memory of this geezer*, Yes, there is a firm reason to believe that “screw” had a sexual context in this phrase.
This does not mean that the act of intercourse was considered to have led to botched work. Rather, taboo terms–frequently based on sexual terms–are often employed to give emphasis to one’s expression and using “fucked up” or “screwed up” originally provided significantly more emphasis than “messed up.” On a sliding scale, “fuck up” would have been, (in the 1940s), the harshest possible epithet while “screw up” would have been been inappropriate for polite company and “foul up” would have been the minced oath that any preacher could have employed at the ladies’ sewing bee.

  • At the end of the 1950s, I’d have gotten a reprimand from my mother for saying something was “screwed up,” explicitly because she did not want any vulgar or obscene expressions used in our house.