I'm getting at least tens of hits per day coming from searches for keywords like error, 0x80070052, and memory card. It turns out that after writing my snarky little post relating to Mark Russinovich's blog post about problems copying files to USB flash drives, I posted with the words "memory card" in the body of the post, and now I'm a keyword magnet. Some people might be game to spin up a Google AdSense subscription, but I'll just say:
If you're getting an "Error 0x80070052" copying files to a memory card / flash drive, it's because you're putting too many files (possibly with very long names) in the root directory of the memory card. Make a folder on the memory card / flash drive and copy the files into the folder. They'll copy fine.