TeraCopy is a 3rd party utility which replaces the standard windows file move/copy dialog for better control over the copy process (skipping on errors, CRC testing after operation, pausing, log of fails/successes). Unfortunately, WinMerge continues to use the standard windows copy operation despite TeraCopy being installed. Since WinMerge copies tend to be the kind where TeraCopy is the most useful (large, complicated, many potential fails/overwrite decisions) this is a bit of a gaping hole.
TeraCopy is likely not the only such utility, but it is a popular one. I am most familiar with TeraCopy, which is why I referenced it in this case. It is a commercial product, a freeware version exists at http://www.codesector.com/teracopy.php