I am running SdFat on my 1284P clocked at 20MHz and most of the time, all works fine. Not all of the time though. The SD card is interfaced with a STMicroelectronics 74AC125MTR and is driven by a 3V regulator good to 400mA, so I think the hardware is fine.
If I set it to SPI_HALF_SPEED it is reliable, and it is reliable at full speed on my 16MHz board. I can hack the library so that "SPI_FULL_SPEED" is based upon 16,000,000 instead of 20,000,000 and I expect that will solve the issue, but before I go down that route I thought I would solicit other ideas.