The leap day bug was caused by certificate bug as explained in the blog post on the root cause analysis.
A specific certificate, is given a one year validity range. It uses midnight UST of the current day as the valid-from date and one year from that date as the valid-to date. The leap day bug is that it calculated the valid-to date by simply taking the current date and adding one to its year. That meant that when tried to create this specific certificate on leap day set a valid-to date of February 29, 2013, an invalid date that caused the certificate creation to fail.
Full details in the blogpost: Summary of Windows Azure Service Disruption on Feb 29th, 2012 - Windows Azure - Site Home -