Hedge is very, very strict in throwing errors as soon as detected.
If as much as one file failes copying, the transfer is cancelled and you'll be prompted with a list of the problematic files.
If a copy fails to verify while copying Hedge will continue copying other files. The name of the failed copy is saved. When the transfer completes you'll be prompted with a list of the failed files, so you check yourself if the copy is indeed corrupted.
When running into errors, we think it's best to redo the whole transfer. The file(s) that failed to copy or verify might very well not be the culprit: it's far more likely that your Source or Destination is having issues. By redoing the whole transfer you make sure you're able to detect this: if a disk is having issues, copy or verification errors will pop up again, probably in different files.
If the progress bars turn green, everything has been copied and the copy process has been verified. However, there is always a very slight chance that a hash created during the copy process is not ok, due to disk read errors. No disk, operating system or connection is infallible. Hash errors are only avoidable by reverifying all Sources and Destinations up to three times each. Unfortunately, this is often not an option. It will take ages, so it's a lot easier to just keep your Sources around instead of reusing them. If this is not possible, at least make sure you check all copied footage for playability.
Even though verification is very reliable, it doesn't paint the whole picture: your footage itself might still have issues. Always check your footage by playing back the copied files, to make sure you don't run into issues later on.