If you're unlucky enough to experience memory errors in one of the intermediate buffers files go through while being copied from one computer to another an incorrect copy of the file might get written to disk.
When running software RAID, memory errors could also cause data to be replicated erroneously and raise an error the next time it's read. That said if the memory is flaky enough that these errors are common it's highly likely that the operating system will crash very frequently and the user will know something is seriously wrong.
If you want to make sure that files have been copied correctly you can flush all kernel buffers and run diff -r between the source and destination directory to make sure that everything is the same.
It's probably way more likely to experience data loss due to human error or external factors such as a power surge than bad ram. I personally thoroughly test the memory before a computer gets put into service and assume it's okay until something fails or it gets replaced. The only machine I've ever seen that would corrupt random data on a disk was heavily and carelessly overclocked (teenage me cared about getting moar fps in games, and not having a reliable workstation lol)
I wonder whether something like Syncthing would notice a hash difference with data corruption caused by such a memory error? And whether it’d correct it or propagate the issue…
Data that's about to be written to disk often resides in ram for some period of time - bit flips in non-ECC ram can silently corrupt the data before writing it out. ZFS doesn't prevent this though it might detect it with checksumming.
