... So far I've just been dragging the files over to the MyPassport, but would it be better to use Time Machine on that drive as well?
You can, and it will work, but it's not better idea to use the MyPassport for both purposes.
Dragging files over is OK, but using Time Machine on that same volume is not recommended. The reason is that Time Machine expects to eventually use the entire capacity of its backup volume. This is normal, and by design. Once the backup volume becomes full, Time Machine will delete expired backups according to a clever algorithm.
The problem is that the additional, non-Time Machine backup files are respected and will not be overwritten, but you will encounter a dilemma if you want to copy additional files to that backup volume. There may not be enough space to do that, and manually deleting Time Machine backups is not recommended for a number of reasons.
If you are determined to use the same drive for Time Machine and other files, partition it. Beware that a mechanical or other catastrophic drive failure usually results in the loss of all partitions.
Given the "mission profile" of Time Machine, it's best to use a backup device dedicated for its purpose. An additional hard disk is cheap insurance.
Is there any problem with using Time Machine on an intermittent basis onto a disk that is frequently disconnected from the Mac?
No, not at all. Obviously you should eject it (drag its icon to the Trash) before disconnecting it.
(I've also got cloud backup, but I've always felt most secure with a hard disk backup).
Good idea. Redundancy is always a good idea. "iCloud Backup" is sort of misleading for reasons I can explain if needed, but it's nevertheless a good part of an overall backup strategy.
Time Machine will be fine with backups done only once in a while. It does sometimes pop up notices indicating that your Time Machine backup is overdue.
An alternative you may consider is to run Carbon Copy Cloner or SuperDuper on the portable drive and do a "clone" of your internal drive. These clones are bootable, so if something goes wrong with your internal drive, you can boot from the clone and run repair programs or clone back to your drive to restore it. These clones provide one snapshot of your computer on a given day. They don't provide the versioning that Time Machine provides. Having different types of backups like this is a good practice. For instance, if something went wrong with your Time Machine software setup, you might encounter trouble restoring from the Time Machine backup, but you would at least have the clone made on the portable drive.
What is the size of your iMac's hard drive?
I prefer using CarbonCopy Cloner to TimeMachine, because you can boot from them.
I would also recommend performing backups more frquently than monthly.
Using TimeMachine intermittently is possible, but it would then negate one of it's advantages, continuous in the background backups.
My iMac hard drive is 1 Tb and it has a little over 100 Gb on it now. Very little of that is changed on a regular basis, so I think it will be a while before Time Machine fills up my backup disks.
Just to be clear, Time Machine is continuously backing up the hard disk onto the 3 Tb disk, and I bring in the other hard disk now and then as an added precaution in case of fire or some other problem at home. I'm not too concerned if it is a couple weeks out of date.
Time Machine: Automatic and "sanctioned" by Apple, very convenient, keeps all versions, but uses more space, is tough to manage manually (like if you just want to pull a few files from it but not replace current ones), and is not bootable. I agree with John Galt that you should put your files on a separate partition since Time Machine, unfortunately, cannot be told to only use part of the disk.
Cloning or other automated system (I recommend Carbon Copy Cloner): Bootable if you wish but does not keep previous versions of files. Also not free in most cases, but CCC for Snow Leopard (before it became paid) seems to work fine in Mountain Lion.
Manual copy: No reason to do this unless you don't trust an automatic system. The slowest option since you'll be replacing everything each time or manually finding the right things to copy.
If you are "dragging" stuff to the portable, it
implies you are using this drive as a data backup,
is this the case?
If this is the case, you could use many of the file
backup utilities available on the market which can
compare whats internal to what is external and just
update/add the differences. Most can be set to also put
previous versions of files that have been updated into
If you are comfy with working with command line and
shell scripting, you could also use Apple's built in rsync