It may not be defective. Sometimes the watch needs to be "cycled" before all the features engage properly depending on how it was initially set. I've noticed this with a number of watches.
If it's new you have lots of time before the warranty expires so why don't you use it for a while and see if it corrects. Alternatively, use the correctors to set it for a date for last month then manually move the hands through the month and see it everything sets properly. Make sure you do this at the right time of day (see manual) to make sure nothing is engaged while using the correctors.