The basic plot of a dome with otherworldly powers isolating a town is very compelling. There are a number of mysteries to be solved and we want answers. As in Lost, each episode tends to introduce more mysteries than it solves.
What isn't compelling is an unrealistic small town peopled exclusively with psychopaths and scumbags. From the insulin stealing woman to the abusive kidnapper and his accomplice to the murderer ex-army visitor to the antibiotic incinerating priest, everyone is a complete and utter dirtbag. It doesn't take long to conclude the dome is doing the rest of us a favor by isolating this collection miscreants from the rest of society until they can be brought to justice.
Attempts to understand what is happening are sporadic and random. Once in a while someone has an idea and we watch them try it out. Rarely do we learn anything useful. Most of the runtime is devoted to the kinds of drama that neither requires a dome nor is influenced by its presence. This is unfortunate because the only engaging character is the dome itself. It should feature prominently in every scene.
Five stars for an interesting idea. No stars for failing to give us characters we care about. Flaws we can accept; murder, girlfriend abuse, kidnapping, hoarding insulin, stealing and destroying life saving antibiotics, and so on we cannot accept under any circumstances. These people are deplorable. Five stars.