Not sure why but the Saturday/Sunday dates aren’t displaying on some of the month views in the date-picker.
See here for an example: http://imgur.com/amsPWrV
In the example shown in the above image, if you want to pick Sat, Apr 9, you can find it by stealth by mousing beside the Apr 8 entry. A narrow highlighted rectangle appears and will update the field to the 9th. If you want to pick the Sunday, you would have to enter it directly into the cell or move the month so that April was at the end.
While one can work around this, it’s still feels buggy. I tried it in two browsers (chrome, firefox) on a macbook pro and on I.E. in a virtual machine.