The only issue I can imagine with playing movies off an external drive is the compatibility across OSs of different filesystems. If you're using Windows, you're probably going to want to use either the FAT or NTFS filesystem. The external will be preformatted with one of these two.
The FAT filesystem has the best compatibility across OSs, but it's old and has a number of limitations (most notably, no files over 4GiB). NTFS is more modern, but it's largely a Windows-only filesystem. Linux can read and write NTFS, but I don't think NTFS is as well supported as most Linux filesystems.
There is software to add Linux filesystem support to Windows, but it seems to be limited.
You can also partition the external, and use multiple filesystems on it, but I don't think there's much point, unless you have very specific needs.
Ultimately, for cross platform compatibility, I'd go with FAT, unless you need to store large files.