You should really copy and paste the names of some of the files that won't transfer across, so we can see what the problem is. Fat-X, the XBox file system, isn't as powerful as FAT-32 or NTFS, which Windows uses.
There are at least three differences between what the XBox can use for a filename and what Windows uses:
1. Filenames can be very long for Windows, but are much shorter for the XBox, If you try to copy a file with too long a name onto the XBox then the XBox won't let you, even though the file works fine on a Windows PC.
2. Filenames on the XBox cannot contain some of the characters that they can on Windows. If you try to copy a file with one or more of these characters in the file's name onto the XBox then the XBox won't let you, even though the file works fine on a Windows PC.
3. You can only have so many files in a directory on the XBox, and this sounds like it might be your problem, although any of these three points might be your problem.