As usual, talking heads talk... It's amazing that any EMSer would ever consent to being on a show since every EMS know-it-all will gladly step up on to their soap box to go on about how the subject EMS is awful and then go on about how great they are. As a doctor and former medic... BLS the patella dislocation. I've seen a number of them and they all were manageable for transport with immobilization. It's the reduction that will hurt. I typically don't give them anything because it will reduced in mere seconds and the pain will immediately begin to diminish, maybe a percocet afterwards.
As far as the 14 month old... sure, ALS would have been appropriate, but it's tough to tell whether or not the kid was actually BLS'd (probably got epi at some point, though it is not mentioned at any time) or if she was even brought in by Boston EMS (notice the EMT carrying the child into the room is NOT in BEMS uniform). Even if the pt. was BLS'd, epi-pens are required items on BLS ambulance and the state protocol allows EMTs to admin epi. Epi is, hands down, the most important med, so even if ALS didn't take the patient, she would have gotten standard of care if BLS'd. There is SO MUCH post-production in these shows, the scenes shown are often not in chronological order. They will play a recording of someone "saying A8" in a report to the hospital and show video of A14 and then show video of a person giving a report using a different radio identifier. That stuff is all over the show.