Note: When backing up an APFS-formatted volume with CCC 5.1 or later, CCC will copy files from a read-only snapshot of the source volume. The subject of this article is not applicable in those cases.
Mounted disk images and running Virtual Machine container files pose an interesting problem to incremental backup utilities. By simply being mounted and accessed (e.g. via browsing the contents, booting the VM), the content of these large files are subject to modification by the applications that use those files. If you run a CCC backup task while a read/write disk image is mounted or while a VM container's OS is booted, there is a chance that the disk image file or VM container will be modified while it is being backed up, resulting in a corrupted version of the file on your backup volume.
If you have disk image files or VM containers that are regularly in use on your system, you should exclude these items from your backup routine and configure an alternate backup task for these items that runs when they are not in use. Alternatively, you could quit or suspend the applications that modify those files for the duration of the backup (see the "Example pre and post clone shell scripts" link below for examples of how to automate this).
If errors do occur while backing up large files, quit or suspend the applications that modify those files, then simply run the backup task again to correct the copy of the file on the backup volume.