That strikes me as something that DeForest Research would have caught; now I'm curious to see the report from that episode, if it's at UCLA.
Actually, I'm mistaken. (I was working from memory.) I just checked the script--but the plot thickens a tiny bit:
KIRK:
Gentlemen, this computer has
an auditory sensor. It can,
in effect, hear sounds. By
installing this booster...
(indicating Spock's work)
We increase that capability on
the order of one to the tenth
power. The computer should
now be able to bring to us every
sound occurring on this ship.
So, the scripted line was indeed "one to the..." (not the proper "one times ten to the...." But it was scripted as "tenth power" (yikes!) instead of "fourth power." (I'm glad the booster can't amplify the heartbeats ten billion times. I'm remembering the nurse who dropped the surgical scissors in Fantastic Voyage while the Proteus was in the inner ear.)
Of course, whether it's tenth power or fourth power, it's wrong either way.