Do you have any screen shots of the errors? (use printscreen button then paste clipboard into paint)
Are the symptoms you describe from a specific backup program? Or are you experiencing this by way of drag-n-drop/cut-n-paste with the explorer shell? (using open/explore my computer navigation methods)
This sounds like a filesystem type copying discrepancy... copying from NTFS to FAT16/32 has inherit complications that can be overcome by understanding these limitations.
The assumption is that the Dell Inspiron E1705 running xp media center edition has NTFS and the Acomdata PHDO500USB hard drive is formatted with FAT32. This can be confirmed by right clicking the drive letter in explorer and selecting the 'properties' from the menu, revealing the storage property sheet with usage and FS type info.
Have you run chkdsk? This is one of the best things to do when you have disk i/o issues ... this can be done with the storage property sheet mentioned above or at a command/recovery console prompt using > chkdsk /P /R .. If this results in errors were found and fixed, do the scan again, and again until you see the scan complete without having/needing to make corrections... remember to reboot the system after each scan attempt as changes/repairs by chkdsk won't properly update until system repost occurs.