Although paypal is considered safe by paypal. You also need to remember if you ever call tech support, they do outsource support from India and sometimes do ask for your SSN. I have heard on case of a support rep stealing a users identity. It probably is an isolated case but you never know.
Paypal is secure enough to protect you and your money but you have to be very careful when you login your account.So many scammers use keyloggers or something similar to steal your password.Maybe paypal can use virtual keyboard to avoid this issue.