While it’s still not entirely clear whose fault last week’s iPhone 3G launch debacle was, a new screw-up by AT&T today certainly doesn’t give them any more customer credibility.

The company posted a webpage earlier announcing the availability of free Wi-Fi for iPhone owners at any of its more than 17,000 hotspots nationwide.

“AT&T knows Wi-Fi is hot, and free Wi-Fi even hotter, which is why we are proud to offer iPhone customers free access to the nation’s largest Wi-Fi hot-spot network with more than 17,000 hot spots, including Starbucks. Now users can relax and access music, e-mail, and Web browsing services with their favorite blend in hand from the comfort of their favorite location."

The problem? The page was put up in error, as AT&T told GigaOM:

"We have not made any announcement regarding free Wi-Fi and iPhone.

The webpage was posted in error and is being removed. Wi-Fi is a real differentiator for AT&T and it is our intention to make it available to as many customers as possible, but we have no announcement at this time."

Normally an error like this may be easily forgivable — except that this is the second time AT&T has done this!

A couple months ago I was at a Starbucks that had AT&T Wi-Fi. I opened up my iPhone’s web browser and was greeted by an AT&T splash page to enter my cellphone number. I did and was granted free Wi-Fi. I went back the next day and it was gone.

For those keeping score at home that is now two mucked-up launches that AT&T has been involved just this month.