“Failed to copy D:\RemoteInstall\SMSTempBootFiles\P01000D8\Windows\Boot\Fonts\segmono_boot.ttf to D:\RemoteInstall\Boot\Fonts\segmono_boot.ttf”
and
"InstallBootFilesFor Image failed. 0x80070003"
error messages could be found. The error message "The system cannot find the path specified error 0x80070003" pointed me in the right direction. The “D:\RemoteInstall\SMSTempBootFiles\P01000D8\Windows” folder was missing on the distribution point.
The solution was quick and easy. The missing folder had to be copied from a working DP and after the WDS service restart the DP was up and running again.