Fiddelysquat: You can still be logged in on two different browsers on two different accounts on the same computer. That usually works fine. Try it. I just edited my first post to clarify that I was referring to two browsers with the same account – that doesn’t work any more. For transferring pets, if you want to be cautious (just in case), then refresh your receiving page each time just before you click on the abandon page, to be sure you haven’t logged out. And then of course refresh your receiving page again after each click on the abandon page, to adopt the pet. Also, remember to have more than enough neopoints in your adopting account!
Thegreenside: I’ve been trying to duplicate your neomail icon glitch, but I can’t seem to. I log off FF on my main and go to a different site; from my side on IE I send a neomail to my main; on FF I go to Neopets main page which shows I’m not logged in; I click Login, then log in; but no mail icon shows up on the Log In page or the password page. As soon as I get to the Pet Central page, I see my mail icon.
Maybe it’s my version of Firefox? I couldn’t get it to show the mail icon before login in IE either. I’m using Firefox version 1.5.0.10 and IE 7.0.5730.11.