The loan officer took the Uniform Residential Loan Application by telephone. The loan officer signs and dates the application
(page 4 of 5) the date he takes the application by telephone. On the borrower's signature block (page 4 of 5), what date should that be? The date the application was taken over the telephone or the date the borrower came in and signed the application?

I don't think it matters much what date the borrower uses. For HMDA purposes, (at least the way I do it), I use the date that the application was taken, (if phone or face-to-face), or received (if mail) by the Loan Officer.