My car entered production on 12/2 and was delivered on 12/16. When I made my first supercharger attempt, I found that I could not get the cable to latch, no matter how hard I pushed it in. I asked the person charging next to me if he could help a newbie. He couldn't get it in either. Fortunately, the supercharger was at a Tesla showroom, which was still open (6:30 pm). Service was closed, but one of the staff came over; she warned me that it would look like she was going to damage my car but assured me that she wouldn't. Then she took the handle and shoved it in and wrenched it left and right in what I will call a "spirited" fashion (which other might describe as violent), while applying force into the receptacle and it finally latched.
I have now been able to replicate this work-around myself and get it to work a few times by practicing there and at another supercharger where I stopped only for practice (so I will not be stranded unable to charge when I actually need it). I am hoping it wears to become easier with time. Hopefully, once Tesla gets wind of the widespread problems, they will replace these uncooperative charge port parts in production (and service) with something without the problem.