Frankly, if you are unwilling or unable to use ECC RAM I would not consider using a self-healing file system such as ZFS (as discussed in the linked forum post) or Btrfs.
The reason is simply that the "self-healing" features quite easily can become "self-destructing" if there is a RAM problem.
Instead, on a non-ECC RAM system, you would probably be better off running a regular file system such as ext4. With Btrfs' state today (starting to become stable, but still a number of rough edges that need smoothing out and has yet to see significant real-world deployments and experience with failures), this would make me feel a lot more comfortable. Even ZFS, which is relatively proven as a file system, still has some glitches on Linux hosts; Btrfs isn't as mature as ZFS.
To detect bit rot on a file system that does not have the ability to natively validate data checksums, you can use any of a number of tools available for that purpose. One such tool, which I am not affiliated with, is hashdeep which can do MD5, SHA1, SHA256, Tiger and Whirlpool hashes. If you run this on a reasonably regular basis (same as you would a ZFS or Btrfs file system scrub), then you can be reasonably certain that you will catch any degredation that might happen. You can then restore the affected files from backups, either on-site or off-site.
I am not familiar with Crashplan, but I suspect they look at file metadata to determine if the file has changed or not, and since the file metadata likely won't be affected (unless it just so happens to be the target of the corruption, which will either be relatively inconsequential or cause any hash validation to also fail) it shouldn't be detecting any changes to the file. Hence, corrupted files shouldn't get backed up. If you want to be sure, configure your backup solutions to keep at least a few old revisions available in case one gets corrupted and backed up in such a state.