Is it possible to check for bad sectors (read error) for a disk with unknown partitions?

Solution 1:

Yes. Use ddrescue for this purpose. Copy into the Null-Device and use a log file. ddrescue knows how to handle read errors!

The log file will finally list all unreadable areas on the source drive in absolute addresses. You just have to divide them by the numbers of bytes per sector to arrive at the sector number.

I am not aware of a similar tool for windows.