I'm not a Mac person, but files can become corrupted on a USB stick if you remove it while the computer is communicating with it. On a PC, you'd right click the USB stick and choose Eject. You'd then get a message that it is now safe to remove. There's probably something similar on Macs.
Apart from that, I would use Dropbox in your situation. Much easier.
Make sure the USB stick is formatted FAT32 and do that on a Windows PC.
Many thanks for the responses. Sorry for this late reply. I formatted my memory stick using FAT32, however it only worked for me when I did a full format as opposed to using Quick Format.