As I said earlier, this is definitely an issue at Paypal. I opened a case this morning and they confirmed my suspicion.
To be more complete, here is a copy of the reply that I got from them this afternoon at 3pm GMT.
Thank you for contacting PayPal Merchant Technical Services.
currently we experiencing some login issues and as result some of the customers my have trouble with login into checkout.
Our research team is working on this issue as priority .
Unfortunately at the moment I do not have any fix time.
I will let you know as soon as I get any update from them.
My sincere apologies for any inconvenience caused.
Feel free to come back to me answering this email for more information,
Merchant Technical Support
Hope this helps.