probably as safe as any other sort of account (depending on who's providing it). A lot more "safe" than credit cards, where you just need a number and an expiry date to do quite a bit with it.
Yes - I had an awful time trying to apply for a cahoot account. I thought their customer service was terrible and they were very rude.
I had a much better time with the Halifax who immediately opened a current account with a similar rate of interest. They customer support appears much better. You also have a real branch if things go wrong.
I also have an online ING Direct savings account, and they were fine on the occasion I had to talk to them.
Personally I'll go online if it saves me time or a reasonable amount of time, providing the customer support is sufficient.
cd