VideoGamesUncovered's Ian writes -
"So I went down to GAME all kiddy like a school child to pick up my brand spanking new Xbox One. Did the standard queuing up, chatting with other consumers and what not before leaving the store as the proud owner of not one but two Xbox Ones (one for me, one for a friend)."
Resolved: Xbox One was replaced by GAME within 24 hours of requesting a new one from head office. Failure rate from my store comes out at about 2.5% though obviously that's a small sample size.
GAME are offering replacements though your local store may not have the stock at the moment. Once you get a reference number, a replacement will be sent to your local store asap.
GAME support recommend anyone with the issue first try running the console upside down as this has corrected the issue in some cases (seems to be a loose part that needs shifting out of the way or something).