Assuming that the attacker doesn't have access to your system with the necessary permissions to read raw disk devices (
/dev/sda and the like), and that he/she doesn't have physical access to the disks, I don't think it'd be much of a concern. As chris pointed out, the problem discussed in the article (with reference to Linux and plain-text passwords specifically) is that a password which is stored in RAM as cleartext (as it necessarily must be at some point*) could be part of a page that gets swapped out to the disk, and thus it could wind up being readable from the free space on the disk. But Linux uses separate partitions, i.e. physically disjoint parts of the disk, for swap space and file storage (unless you've configured the system to use a swap file), so an attacker who can access the disk only through the filesystem wouldn't be able to get at the part of the disk that holds swapped-out data.
If you want to check for passwords being stored on disk, in readable files, in the clear, I'd take a look at things like your web browser's password manager, and the configuration files for any programs you ever enter passwords into.
*for normal algorithms