Update: I got a call from Tesla Springfield on Tuesday saying that another car was a available with the same specs, so I went over there the same day to check it out. When I got there the delivery person started off by telling me that I was not allowed to spend as much time checking the car out as before. The reason he gave was because the car was not allocated to us at this point (although you have to wonder whether he just wanted to make it more difficult for us to find issues with this 2nd car by limiting time to look it over). So I asked him to allocate it to me and then started working through the checklist as quickly as possible.
This Model Y was in much better shape than the first car, so I scheduled delivery for 11am the next day (tesla delivery guy said they needed time to detail the car and get paperwork ready).
The poor customer experience didn't end there unfortunately. At 20 minutes before the pickup time, while my wife and I were driving en-route to Tesla Springfield, they called to say that the car would not be ready by 11am as scheduled because they hadn't detailed the car yet and we had to come at Noon instead.
After killing another hour, we arrived, called, and we were told to head to a line of parked Tesla's where they would toot the horn and unlock the vehicle for us. We got to the car - no horn. Waited 5 minutes - no horn. Unable to get into the car to get to the documentation we called again. Call went to voicemail. After 3 calls someone finally picked up the phone and unlocked our car.
The car was clean, but they left the glue residue in the trunk and all but one of the paint chips.
After signing the documentation, we went inside the Tesla office building to try to find someone to explain what to do next. Eventually found someone who took the whole packet of docs from us and said we were done and could leave. I thought it was strange that we didn't even get a copy of our signed docs, but he insisted that was the correct procedure. Seems he was wrong since they had to email the copies to me today and the delivery guy who called said "yeah, the person you spoke with probably wasn't familiar with the process, and sometimes things drop through the cracks".
Here's the issues I documented with the replacement Model Y:
1) AC Compressor Acoustic Cover missing and needs to be installed
2) Non-aligned rear seat (although not as bad as before)
3) Sticking out tail light
4) Glue residue in trunk in 2 places
5) Small paint chips/blemishes on
a) Front bumper
b) Top of passenger side mirror
c) Driver side rear door
d) Driver side rear panel
e) Passenger side front door hinge
6) Trim scuffed on rear driver side behind the wheel
I would say that based on my experience, every Model Y is highly likely to suffer from all the above issues to some extent or another. It's best to raise and document the issues before you drive the car away so that you have a case for Tesla to fix any issues in a subsequent service appointment.
I'd also say that some Tesla locations seem more competent than others. I have found Tesla New York to be amazingly good in terms of communication, treatment of the customer, knowledge and helpfulness. It was actually my Tesla NY sales contact who found the replacement Model Y for me (not Tesla Springfield). He really went above and beyond to get things back on track. As for Tesla Springfield NJ - let's just say there's room for improvement.
Having said all this, I am now enjoying my new Model Y.