Just going to bounce around in bliss.
Energy:
The world if facing an energy crisis. There is a massive need for cleaner, more efficient, and better distributed electrical generation. From everything I've seen, humanities best bet is Fusion. Look it up. H-H fusion produces gigawatts of energy with the amount of hydrogen contained in bathtub worth of water, and produces only Helium as waste. There is no risk for catastrophic failure (i.e nuclear explosion/meltdown like Chernobyl , so the process is inherently safer than Fission. If you're curious, look ITER, its a Fusion test facility being developed by the EU in France. This if far beyond the silly "sun" fusion thing they did in spider man.
I agree - however, the manifestation of 'New Energy' is going to spawn another Industrial Revolution-type ripple when it occurs. Also, is this a strictly necessary avenue of research if Germany, as a country, might remove themselves from the grid as early as 2025?
Disadvantages: not a quick fix. Will take decades to produce a facility capable of producing this kind of energy on a commercial scale.
Once scaled up properly, there will be almost no cost to produce clean energy for the world. Problem: What happens to the world economy when energy is free?
Remember in our thought experience, we're not restricted by the usual bureaucratic and academic infighting - so decades could be brought under ten years if the research was attacked obsessively from as many possible angles.
Problem Response: An free-energy world is also a post-economic world, I think. Otherwise,
unlimited energy won't be free.
Crude oil:
Gas for cars: An issue a lot of people know something about, but few people know a lot about it. Maybe I'll come back to it. All I'll say right now that an alternative from crude derived fuel needs to be found. That will take decades at best, and the longer we wait, the harder it will be to transition.
Your second point for crude,
plastic, is by far the most poignant.
Let's adjust the first to:
Mobility Vehicles: What other modes of transportation are available to serve the same purpose as cars (whether that means alternative fuels, Musk's
Hyperloop, or anything in between)?
Plastic: Crude makes everything, and thats an issue. Way beyond gas powered vehicles, Nearly everything made of plastic comes from crude oil. This sucks, because regardless of how much you believe there is, it will eventually run out and/or it will/is becoming exponentially more expensive to get. Even if we figure out how to replace fuel, there are almost no alternatives to non-crude derived plastics. Lactic Acid can actually produce some decent plastic, but its a yeast based biotechnology and would be hard to scale up.
Like with fuel, we know crude will run out eventually. Not for a while yet, but again we need to start now because the world runs on crude, and it will take a very long time to change that.
As I wrote, the much more critical issue when considering our use of crude fuels. Not a lot of people realize this; all our tacky, crap plastic filling landfills are the human transmutation of the majestic, awesome fossilized bones of that which has came before (especially dinosaurs

).
What am I going to do without cheap crap?
This feeds into the idea of planned obsolescence, which I think we should ignore for the purposes of this conversation. Let's assume that alternatives can be made-to-last and environmentally resistant.
Space:
The long term survival of humanity requires space exploration. The earth will eventually become inhospitable and run out of resources. To steal Neil deGrasse Tyson's idea: lets build afleet of launch vehicles that can take us anywhere in the solar system. One that can get us to the moon, to venus, to mars. Figure out how to build orbital platforms on the moon, mining platforms on astroids, space stations around mars.
Why space? Eh, theres another thread for that
.
Anyway thats a few quick thoughts.
No, this topic definitely deserves to be included here as well to consider generally.
Legalizing pot maybe? It sure has many different uses. First of, if you start taxing it, the black market will be weaker, and lots of "new" tax dollars can be spent on other things. It can be used in textiles, paper, paints, clothing, different foods, cosmetics, insulation, animal feed, medicine, and many many other things. I even heard that it can be used as gas, but I do not want to claim that 
I am not saying that this will save the world or anything, but it is well worth to legalize it, so we can research its potential without prejudice.
The potential of the plant is huge, and it is a shame that we do not take advantage of it.
Lol - Jack Herer's
The Emperor Wears No Clothes?
You're bring that one historically full circle, Royce. +1 the bold. Also, I've read (and studied) elsewhere corroboration for the idea that THC is only one of as many as 4000 possible compounds with medicinal properties in hemp plants (research has been slow before and since the mid-70s).
Immortality.
Check out Aubrey de Grey, Google's Calico, or, obviously, Kurzweil (who was hired to build Google's attempt at an electronic brain, among more mundane projects).
On research into how we don't lack the solution to a bunch of current problems, instead it's just that various minute demographics simply choose to deny the already present solutions to various other peoples. And how those other peoples treat it as if it's a condition of nature (ie, unchangeable) rather than the choice of other men.
More sociological research then

? I'm sure in our hypothetical world, science is maximally efficient, so we can easily gather the relevant census data and, of course, have organized access to all available research data (which seems the largest obstacles to finding evidence one way or the other).
On research into how we don't lack the solution to a bunch of current problems, instead it's just that various minute demographics simply choose to deny the already present solutions to various other peoples. And how those other peoples treat it as if it's a condition of nature (ie, unchangeable) rather than the choice of other men.
... not a big mystery. Money. Who is going to spend money to save people without it?
Well - everyone in this thread?
Also, no one is forcing you to spend your imaginary research money here. Feel free to hold onto it.
Lol. We're all infinitely wealthy for the purposes of this thread. Inaction is not an option

.