Q: Calendar is showing the wrong date in my dock

You could remove it from the dock by clicking on it and hold. Then drag from dock and un click. Then go to the top go menu and open applications. Right click on the calendar and then make alias. Insert the alias in the dock.

Then something in your user account has modified ICal. Try this link.  https://discussions.apple.com/thread/2607509?tstart=0

Here is something you could check on.  https://support.apple.com/en-us/HT203413  Also this.  https://discussions.apple.com/thread/2607509?tstart=0

Same problem here: today is 28 January, but iCal icon shows 25 Jan.  Never had this issue before.

Is your date and time set to automatically update in System Preference> Date and Time.

does the situation remain the same when you restart the mac

I had the same problem, the dock icon would not update to the current date. Quitting and restarting the Calendar app had no affect. However if I opened the date and time control panel, and unlocked it, then the dock icon updated to the current date.

I also notice if I leave the Calendar app open the date does not update on the main calendar window, but it does in the mini calendar.

Running OS X 10.11.3

It may not solve the problem, but this is what happened to me:  I have two MacBook Pros.  Both have the same problem and each morning I have to run Killall Dock in Terminal to correct the date on the dock.  Then yesterday I took delivery of my new 27" iMac.  Set it up in minutes, spent late yesterday evening and the early hours of the morning with it and the date appeared correctly on the dock after midnight.  The two MacBooks and iMac are all running the latest version of El Capitan.

I wonder now if this could be a problem only for certain devices.