Meaning and acceptability of "One fifty" when speaking of dollars
Solution 1:
In any discourse, speakers measure numbers of this sort by a (presumably) common standard. On the Chicago Board of Trade, for instance, soybean, soyoil and soymeal prices are quoted on three different scales, but there's no problem, because everyone knows what they mean:
Beans quoted in cents and eighths/bushel, so 1341'6 = $13.4175/bu
Meal quoted in dollars/ton, so 341.3 = $341.30/ton
Oil quoted in cents/pound, so 54.82 = $0.5482/lb
Accordingly, "one fifty" does not "unequivocally" mean $1.50. For instance, if you were buying a new cellphone and the salesclerk quoted a price of "one fifty", you would almost certainly understand that to mean $150, not $1.50.
Observe that in the dialogue you quote, the parties do not share a common standard. The second speaker has to demand explicit clarification.
Solution 2:
"One fifty" can mean $1.50, $150, $150,000, or other amounts depending on the context (candy, a paintball gun, a house).
Solution 3:
If you listen carefully, the narrator is not saying "one fifty dollars," which would be quite uncommon. Coincidentally, the quote in question appears at about 1:50 into the clip:
If I could sell my vote, I probably would.
How much?
How much? Psssh… Umm… Like, one fifty? One fifty. (laughs)
A hundred and fifty dollars?
I… I just… I feel like that's even too much. But I wouldn't take any less.
The order of magnitude implied for "one fifty" varies greatly depending on context, which is why the narrator is asking for clarification. Is your vote worth as much as a candy bar? A nice shirt? A (used) Audi R8? The Spelling Mansion? The Rio Tinto mining company?
If we are discussing home purchases, and I say I am looking to buy a house in Northern Virginia for "five-twenty to five forty," I do not mean $520-540 (Detroit might be another story). If I then sigh and say "but nothing near the Metro is going for less than three-quarters," I clearly mean three-quarters of a million dollars ($750,000), not three quarters as in the coins ($0.75). Candy bars might be a different story.
Solution 4:
Here in India, it is actually common for 'one fifty' to mean 'one hundred fifty'. That is, we are not changing units of parlance in this case like we might change when talking in bigger numbers, e.g. 5-6 instead of 5-6 thousand (talking in terms of thousands, understood by both speaker and listener).
Rather, we are actually dropping the hundred to shorten it to 'one fifty'. I am surprised it is not this way in other places. And curiously, this doesn't follow the pattern of Hindi (dominant language in my area), since equivalent form in Hindi would seem downright wrong, not just odd.