We are looking at purchasing some loans from another bank. One of the real estate files has a flood determination in it that is dated 3 days after the loan date. Is there something we can do to rectify this if we purchase this loan, such as ordering a new determiation prior to the purchase, or could there be any recourse against us?

I don't think ordering one now would amount to anything. I also don't believe your institution will be held accountable for the error.

Is it in a flood zone? If not, even better (at least technically)

Joker is right. There's nothing you can do to fix it now. I would document that you caught this.

If it is in a SFHA, I would require the other institution to give notice and require insurance BEFORE you purchase the loan.