Don't know if other 2013 owners have had crazy, squeaky, chattering wiper problems (not a small issue in Portland, OR). I was going nuts and the dealer tried new blades, adjustments and eventually a NEW windshield and it was still ridiculous. A couple of weeks ago they swapped my 2013 arms and blades for the 2012 style - perfect! Let it rain.

 

I also live in Portland and drive a 2013 JCW. I had a similar experience a few weeks ago on a trip to Seattle. The blades were literally dancing across the windshield leaving black skidmarks every few inches.
I stopped several time to try and clean the windshield with only limited luck. Finally found a auto parts store and grabbed a clay bar.
Worked like a charm! Since you actually had your windshield replaced (crazy) I doubt this was your problem, but for future reference this is a great solution. I keep a small piece of clay in my car for any future problems.

 

The clay was tried as well as steel wool and razor blades...I can't believe they replaced the whole windshield. The service guys really thought they'd eliminated all the other options. I was told they had a couple of other 2013s with similar problems but that mine was the worst. Seems unlikely to me that one car would be so different in this respect. Hopefully it isn't a widespread problem but the fix is easy Kudos to MINI of Portland for being willing to keep trying when they probably could have blown me off.