I applied for a new account for my mum three weeks ago in anticipation of her being able to use it for her upcoming trip of two months, which she is leaving on Sunday. 
Whilst the online application was fine and we got an application number, the next step to verify her identity online did not work - it simply did not load (basically gave us a 404).
Calls to Citibank ensued and mum ended up verifying her identity by bringing a relevant application to an Australia Post office.
Up to now we have not received the card, even though we were told 5-7 days. Yes, I realise we have just had a string of public holidays, but it is well and truly over 5-7 working days counting from the date of application. 
A follow up call was made a few days ago and the reply was that (putting aside all the need to hook mum up to talk; apparently her giving me consent to handle her account on her behalf was misguided) we were stil expecting another 5-7 days! They said they would expedite the application; I'm not expecting Mum to leave the country with card in hand.
If it wasn't a useful and trivial account, I'd be telling the last of their incompetent sorry excuses for customer service officers where they can put their account.