My parents were watching a TV show (the show is Arrow, I believe) and in the show, one of the characters said something along the lines of "you're wasting both of our times." They came out to me and asked me if I thought it should be the "time" or "times," because neither of them were quite sure what it should be. I wasn't sure either, but I thought "times" seemed a bit more correct.
What is the proper word here?
As others have commented, the expression wasted both of our time/s is very awkward, whether "time" is made plural or not.
It would have been far preferable to have said,"you're wasting our time."
I also believe that "time" is the correct choice. It is not a "count noun" that could be pluralized, as the word "chairs" in "You have broken both of our chairs." "Times" is a conventional word, however, in certain expressions, as in "These are good times." In that sense, "times" can be thought of as a count noun as in "These are good days" "Or those were favorable periods [of time]." But in your question, I would think of "time" as I would think of the word "money." One could say "You're wasting both of our dollars" (for example, if each person had a dollar bill and each thought that you were spending them on something frivolous), but one would not say "You're wasting both of our monies." (Though, again, there are certain contexts in which "monies" would be correct.) But as the character did not specify that the other was wasting something countable, like "hours," then the choice should have been "time," and I would have said it as "You're wasting both our time." See https://owl.english.purdue.edu/owl/owlprint/541/
I agree with @Livrecache “You’re wasting our time” is the correct way to say it. However, it’s not as punchy as “You’re wasting both of our times”, where “both” is the key word. It compromises on correctness but has more dramatic effect.
