I'm on the third season, and there are few things I've noticed that just don't make sense.

1. Aiden not feeding after coming back from desiccating: after being dug up, he was drained of some of his blood to sell jars of "pureblood," and after being sucked completely dry by one of the Dutch, he almost dies, but he survives by re-drinking back the blood that was drained from him to store in jars. That should have kept him alive, okay, but at no point in time has he drunk human blood, yet he's walking around right now like he hasn't just starved for over a year. How?
2. Badgering Josh to prescreen patients: this plan makes no sense. Even if Josh were to confirm that a patient walking in hasn't contracted the virus, the fact of the matter is that this patient is currently in a hospital, a place for gathering the sick, and could have gotten infected the second they walked in the door. This risk is why Henry isn't trying to get his girlfriend back; if she could get infected just walking down the street, how is picking someone up AT A HOSPITAL not an even greater risk?