I drink between four and six Diet Coke cans a day and have never noticed that they have an expiration date.

I am an avid diet coke drinker and you can absolutely tell when diet coke is no longer fresh. It isn't always by the expiry date (which isn't really an expiry date). As others have said, if it was stored somewhere at higher temps, it changes the flavor. Also eventually it gets old tasting - cans don't really go flat for a long time but the taste changes.

Diet coke tastes different depending if you buy it in cans, plastic bottles or from a fountain machine.

I can say that often diet coke still tastes great long after the best before date. Other times, I have had terrible tasting diet coke that hadn't even reached the date.

Taste it. It isn't going bad from sitting in the can a few extra weeks. It is mostly chemicals.

It might be slightly flat but definitely no danger in drinking it.
It's not that far expired - it might be just fine