3.0.5 was just released which fixes this bug completely.
Very good!
So, to recap, if we upgrade to 3.0.5. we can run Electrum and browse the web or run other apps at the same time safely, with no worries, right?
Also, why Thomas is not speaking in this thread? This is one of the worst problems in the whole Electrum history and it's strange its main developer wrote nothing about that here on bitcointalk...
He and the other developers were busy fixing the bug. He's said he will put out a statement soon.
The bug mainly affects people with no password on their wallets. If you have any sort of strong password like 10+ mixed characters you are safe.