People being there on a Sunday actually reads as one of the more believable things to me. I studied under a few people mentioned in the book and they were absolutely going in on Sundays if patients needed it or to catch up on paperwork.
This show does take creative license to create some really stupid plot points, and I hope they're able to grow up the writing in Season 2 a bit. The ambulance response time is what drove me batty. I've had to call ambulances to lower Manhattan twice (do not do sports near me) and both times were incident --> hospital in under half an hour. And that includes 10 minutes of bullshit w/ building security letting them in. And that's not even getting into why the fuck Max had to be told to dial 911.
And even with all its faults, I do find the show incredibly compelling. Perhaps it's only because I have various personal and professional connections to Twelve Patients, but this show has the potential to bring things boiling under the surface of NYC up to the mainstream and into public consciousness. So even if they do some stupid shit along the way, I'm glad they're doing it. I just hope they dive more into the prison ward next season, it was a huge part of the book, and it feels like a real disservice to the "inspired by" tagline to ignore it like they have this season.