This is one of my biggest fears when it comes to Tesla, and I don't get why it's such a big deal for them to address.
Elon talks about production (and not design or development) being the biggest challenge - apparently its customer service and end-point quality assurance.
While there is no doubt Tesla could be better, remember that people dont go out of their way to post "Had car serviced, all went well" type experiences, so you are looking at a somewhat biased sample here (and, as other have noted, you will find equally bad examples of service for most car brands in the appropriate forums).
For reference, I've had 3 service engagements with Tesla over the past 2.5 years:
1. Got an odd "GPS antenna failure" error. Booked an appt for next week to get it looked at. The error went away next day (probably a software glitch). Cancelled service appt. Got a text from service center asking if all was ok, I reassured them that the error had gone away, replay was "great, rebook if it comes back".
2. Decided to pre-actively replace my 12V battery after 2 years, booked a service appt (5 days ahead). Got a text asking if battery was causing problems, explained that I was being proactive, and was fine paying for it. Mobile service turned up on time, changed the battery, checked tire wear, topped up windshield fluid, and was gone in 30 mins. Paid on iPhone app, zero hassle.
3. Got "creaking suspension" issue. Booked service (6 days ahead). Dropped off car, guy said yep was a known issue they would replace ball-joint and re-seal others. Four hours later, care was ready, picked it up later (just got Uber, walked to car, jumped in, drove away). No charges, all under warranty.
Now, I've no doubt the horror stories posted here are true, and Tesla needs to get better, but certainly my experiences (so far) have all been fine. It's possible my service centesr (Lynnwood, WA and Bellevue, WA) are better managed of course.
For contrast, my Infiniti was broken into last year so needed to get front Windows replaced. Dealer insisted on detailing car (at my expense) "because we can't service it with glass shards in cabin", and then took 2 weeks to change out the glass, after the original estimate was 2-3 days (with zero fall-up until I called them and asked what was going on).