I have seen similar behavior. In my case I have a guess as to what is going on. I will describe what I have done and seen. If this also works for you, maybe some of the unix gurus can tell us what is really going on.
On my Mac Pro 3.1, for data I have a 3 TB WD Red and two 2 TB WD Green disks, and a 480 GB Excelsior PCIe SSD system disk running 10.9.1. I have an iPhoto library which takes over 200 GB. In addition to Time Machine and Crashplan backups, from time to time I have manually copied my iPhoto library onto a different internal disk for backup.
What I have seen is the copy starts fairly slow, with Activity Monitor reporting maybe a few MB/s read and write rates, and Finder suggesting several days to completion. If I do nothing at the computer, after about 10 minutes the copy rate jumps to 80 to 150 MB/s, and the estimated time to completion drops below an hour. If I do nothing and let the copy run, its speed may vary a little but usually it will remain very high and complete in less than an hour as Finder predicted. I think this high rate is limited only by the read and write speeds of the disks. However, if I resume work at the computer, the copy will drop to its initial slow rate and the time estimate of several days returns.
What I think happens is the copy rate is adjusted by OS X depending on whether the user is active or not. If the user is active copy is assigned a low priority (nice) and copies in small data chunks, leading to a slow copy rate. If the user is absent, copy is assigned a higher priority and works with large chunks, leading to a much faster copy.
Other parameters which I suspect may affect the maximum transfer rate are extent of available free memory, extent of fragmentation of the file being copied, and extent of fragmentation of free space on the target disk. Available free memory may limit the size of the chunks copied. Fragmentation of the file being copied may reduce the rate at which it can be read. Fragmentation of free space may reduce the rate at which the file can be written.
OS X varying the copy rate in response to user activity may explain the variation in copy rate seen by dwctv, but not the errors.
dwctv, what do you see if you start the copy and let it run with no user activity? How much free memory do you have? If you quit other applications to release more memory, does your copy reach a higher maximum rate?