While making a payment on PayPal this morning, I noticed a drop-down menu containing a large number of my old addresses (going back nearly 10 years!) as well as addresses for various family members who I'd previously sent presents to. After completing the payment I duly logged in to PayPal to tidy up my account and remove all these old addresses - I didn't feel comfortable, from a privacy point of view, having my life history of addresses stored at PayPal.
After about ten minutes of fruitlessly searching the "My Profile" section for the list of addresses, I decided to turn to Google and, more specifically, the PayPal-Community.com web site. Following the advice of 'CrazyLittle' (in this post) I called PayPal customer services. After a bit of a confusion, they eventually realised what I was trying to achieve. My 'top tip' for you is to say the words "3rd party addresses" and/or "gift addresses" when explaining the list of addresses you'd like to have removed. If your call handler is like mine, then they will keep trying to reassure you that the address currently listed in your PayPal profile is the one they use - but persevere and they should eventually find and remove these "3rd party addresses" from your account.
Given legislation such as the Data Protection Act, I'm surprised that PayPal are allowed (if that's the right word?) to make it this hard to remove old and unwanted addresses from your account. It seems that gift addresses and 3rd party added addresses are automatically added to your profile, but then are not easily removable. I don't see why PayPal won't let you manage this list of addresses via their web site...?
PS. The phone number I used for PayPal was 08707 307 191 - I found this by logging in and then clicking Contact Us in the footer of the page. It gives you a one-off passcode too, which might help speed up the call handling, so I'd advise that route rather than just calling without one.