I did what I could to answer some of your questions, but I don't think I addressed every aspect of the issue. Let me know if there's anything in particular I missed or should elaborate on, or feel free to write your own answer.
Personal Effects - This question reminds me a lot of this one about a worldwide Groundhog Day phenomenon, in that a lot of what people do every day could turn out to be useless. For instance, if you work for twenty years at a job you hate before finally going mad with boredom, you can rest easy knowing that at least you provided for your family-- until you wake up and realize it was all a dream. Just like in the answers to the aforementioned question, this society would start valuing knowledge far more than physical objects. If you read a book in a dream, you should still remember what you read when you wake up, even if you don't have the physical copy. Thus, there should be a greater demand for teachers and storytellers, and various forms of short-lived entertainment, rather than things like decorations that only pay off if you get to keep them around.
Time Travel - Like you've mentioned, the people who've had these dreams have seen the future, and thus once they wake up they have effectively traveled into the past. On a personal level, these people will try to avoid mistakes they made and take advantage of opportunities they missed. On a larger-scale level, these people will be paid to accurately predict things. The accuracy of these predictions will vary: things like the weather are going to be the same no matter what anyone does differently, while the actions of people will change based on two factors: 1) - how long the dream lasted, and 2) - how many people were asleep. If only one guy had the dream, everything should happen as he remembered it, but if half the world had it, things will change almost immediately. However, if the dream lasted a sufficiently long time, there will be a greater length of time where things happen the same, since no one will be able to accurately remember what happened back then. Bottom line is that in most cases, the things you remember are going to stop being useful to you at some point; this could lead to some very sad scenarios, such as a guy who knows he died in the dream, but doesn't know if the world has changed enough this time to avoid it, or someone who found their soul mate in the dream, but cannot find them in the real world because things have changed too much. These problems are compounded by the next point:
Countermeasures - People like to know what everyone else is going to do, but no one likes when other people know what they will do. 207
Thus, when a dream event occurs, it will be the top priority of many people to do the exact opposite of what they would have done. Armies would throw out all of their plans and start fresh, merchants will take a different route through the forest to avoid bandits, passwords and locks across the world will be changed. This is going to severely limit the abilities of your precogs, but only if someone finds out about the dream event. People who can afford it will have a series of 'sleepers' whose only job is to be asleep around the clock (in shifts) and inform whoever's paying them whenever there is a dream event. During their waking hours, these sleepers may actually be sleeper agents, working for the enemy, gathering data to be used when a dream event occurs. When a dream event does occur, it will be a race to take advantage of it before the enemy does.
Religion - There are a few religious problems here, but I don't think they'll matter much. There is the issue of 'why?' but religions have always been able to avoid those questions by making up answers or attributing it to some sort of 'divine mystery'. People may think these dream events are meant to help the faithful, or push humanity in the right direction, or something like that.
The bigger problem is that someone has recorded the future; this has enormous repercussions on the notions of free will, destiny, and such. But again, religions usually have answers to these sorts of things. Either there is no free will (as I recall, this is what some sects of Protestantism argued), or God is just powerful enough to create 'what if' scenarios, but the fact that people change the future after dreaming it means that we do have free will.
Ethics - As you said, people may learn about future crimes, and wish to apply punishment early. But I think we sort of do this already, just with incomplete information. If someone has committed crimes, people suspect they will do them again. If you commit a crime in the future, people suspect you will do it again. But since the future can be altered, these precognitive crimes are just like past ones: the people guilty of them can change, can be saved, can see the error of their ways, etc. 590