A company that's using the contracting firm said they'd pay me $X per hour, and the same amount for hours over 40 in a given week. Apparently there's an exemption from the 1.5x pay for certain engineering positions, which I was told this was. I was (and am) happy with the pay we agreed on.
So the contracting firm sent me a copy of the standard contract to read and sign. But the contract said I was to be paid 1.5x the amount of my normal rate for overtime.
Before signing, I sent them a message saying, "I think this is a mistake." And they came back and said, "You're right, it's supposed to be 1x for overtime." They sent me another copy, but it had the same mistake in it. At that point, I signed it since we were on the same page regarding the terms even though it was still wrong. My thinking was that it was just a piece of (digital) paper that was wrong, and in my favor anyway. The actual contract (the intangible agreement between the two parties) was correct and mutually agreed upon.
My question is, with the contract as it stands, is there any risk that I am taking by not fixing it? I'm getting paid the amount I expect (1x for overtime) and have no intentions to pull more out of them just because the written contract is wrong. I don't want to be in a bad situation, but I don't want to go through the hassle of changing something that doesn't matter either.
Note: I live/work in New York state