The ones you buy in the Gold Saucer for MGP aren't tradeable, so the system won't let you buy it if you already have it. If you attempt to buy it, it will give an error message to the effect of "You cannot purchase another of this unique item." You can check which things you have by attempting to buy each and seeing whether it gives you a confirmation box or an error message. (Works for hairstyles, minions, mounts, etc. so long as they're unique/untradeable.)

That doesn't work for the tradeable ones, however.