My impression is that the service centers themselves are staffed at reasonable levels. We've been very pleased with our interactions with on-the-ground service personnel, on the vehicle side and on the energy side.
Where I think Tesla has skimped is in the national-level call centers. As a result, there are long hold times when customers attempt to call for sales support and about vehicle issues, and no, the app and a bunch of FAQs can't possibly address every concern that people call about. Tesla Energy suffers from the same problem, whether you're calling for sales or service. Also, Tesla does everything possible to make their phone number hard to find; they really don't seem to want anyone to call.
The good news is that this should be relatively easy for Tesla to fix. Staffing up national call centers should be much easier than, say, correcting systematic issues across all of the service centers. I think Tesla's sales will continue to grow regardless, but there will be less pain along the way with improved customer communication.
Regarding
@neroden, I do miss many of the insights he shared, but he was over-generalizing from his own sub-par service experiences and he stopped adding value here when he incessantly harped on this. He always had a tendency to harp on "pet" issues that were of little importance in the grand scheme of things, like bugs in USB music playback and the then-lack of Superchargers in North Dakota, but he just couldn't see past the service issues.