Music only plays for a second and then ends? When I successfully copy my music to my SD card, each song only plays for a second and then continues onto the next song. I was able to remedy this by copying each song over individually, but obviously this is untenable in the long-run. Might this be an issue with my new SD, am I copying too fast, or what else might it be?

I was able to replicate this for skipping to the center of a song. I can't hear an entire second, but it does seek to the center of the song and play a bit of it. If I try to go back to the beginning of the song after every skip, the Music Player eventually crashes.

For any of the mp3s with these issues, if I restart my phone it deletes these songs.
The most obvious explanation is that the file is incomplete: there's only a small fraction of the file there, or only the first section of the file is readable. Given that the symptoms you report in your other question point to SD card failure, that seems the most likely cause for this too.

If this is a different SD card, it could be that the card itself isn't at fault: rather, whatever you're using to copy files to the card could be corrupting the filesystem, or a dodgy USB connection to a card reader could be interrupting file transfers.