Technologically we would need to cover six key areas.
1) Rockets.
Launch capacity is a problem. At the moment I think NASA could have a system in place by 2020 that could manage a moon shot with substantial cargo. At considerable expense. I don't actually think that there will be a private rocket with such capacity in the same time frame without extreme government commitment, which honestly brings in it's own problems. But that's not for this section.
More important is needing a method of getting people and goods to the moon
reliably. We are probably talking a higher reliability than any other launch system that has existed to date. The numbers here are actually
pretty scary. The US averaged between 87.5% success in it's launches between 1957 and 1999, going up to 93.7% in the last decade of the millennium. The USSR/Russia actually did better, scoring over 90% in all decades and getting over 95% after '99. But that's still almost 1 rocket in 20 failed.
Any moon base is going to be reliant on a lot of rockets reaching it. Even if we could send all the people in one trip they would be needing supplies for at least some start-up period. I don't think there are many scenarios where we aren't going to be up against the reliability numbers for any rocket humanity could plausibly build in the next decade. Reality is we would have to expect to lose one or more shipments, be they of people or essential supplies. Which brings us to number two.
2) Manufacturing base.
During the Apollo project, 17 Saturn V rockets were built. That was enough to put people on the moon two by two, without any long term supplies or resources more substantial than the lunar rover. Even converting every gram of return capacity to survival gear, a single Saturn V sized rocket is unlikely to sustain any crew for any serious period of time. Add into that redundancy (we are going to lose some and maybe need the occasional emergency launch on short notice) and large called for lunar population. We are going to need lots and lots of rockets.
The USA is going to need a massive and long term rocket manufacturing base. This is probably not a bad thing, economically or politically (again, get into that later). But it means a massive tooling up period across the nation and some retraining and skill development. It's going to feed into the rocket design as much as the primary concerns of power and reliability.
3) Long term food (and general biological issues).
This is going to need a substantial lead time and even then at least the first few years on the moon would be entirely dependent on supplies from the earth. We need to develop and impliment a robust and diverse food ecosystem that satisfies human dietary needs.
This is a far bigger problem than often given credit, mostly because it's usually us physicists who deal with these questions and we tend to neglect biology somewhat. The problem is biology is messy and complicated. A human is a big ball of cells, not all exactly human in the usual sense. We have a massive and diverse gut flora to take care of, while needing to make sure that they all place nice with any other lifeforms we are dependent on. Odds are there won't be much room for error or experimentation unless we want total dependence on interplanetary shipped food. And frankly we are going to need the option to airlift in a year's food when needed, if something goes wrong with their crops or a disease strikes.
Not a problem I feel placed to even try to solve.
4) Long term air.
Probably as solvable as launch capacity. But it's an interesting question of how to maintain an atmosphere in hard vacuum indefinitely, through changeable conditions (at least night and day) and with plenty of potential for natural disaster. Mir lasted fifteen years, twelve of those occupied. That's not bad start point, but we would need vacuum seals that can last for generations, not just years.
As I said, I'm fairly comfortable in this area. We have lots of experience playing with vacuum. But one second's negligence or one minuscule oversight could cost dozens of lives. We would need (again) massive redundancy and incredible engineering on every last detail of any facilities in order to minimise risk, and even then accept that problems will occur and have extra procedures and facilities in place as fall-backs.
This problem is only going to scale with population and living space. Every individual is a safety risk, every cubic meter of air an engineering challenge. Design and manufacture of every last detail of any facility is going to be massive.
5) Moon industry.
There have been proposals for mining and manufacturing things on the moon. I'm not entirely convinced on any of these. Building ships for further exploration makes more sense outside the moon's gravity well (asteroids are an equally, if not more interesting source of materials) and I don't think He3 mining is going to be as profitable as many other people do. But we are probably going to want to do these anyway even if they only benefit lunar residents and not anyone stuck back on earth.
At the same time we are going to want to develop and discover other things that make a moon base worthwhile, if only to give the population employment beyond keeping themselves alive. This is going to mean developing new technologies to facilitate whatever they are going to get up to. Ideally I'd want to offer almost anything that could be done on earth as an option on the moon, developing whatever is needed to work in low gravity. For starters you focus on things that would be more efficient, but for a long term project you would want options, not utilitarian efficiency and marginal efficiency.
6) Remote construction.
Let's be frank. Putting people on the moon to build themselves a colony is stupid. We would likely want the first several waves to be fully automated. The first people should only need to cycle an airlock and suddenly be inside a ready-to-live base, complete with plentiful provisions and facilities to support a decent sized seed population. Otherwise we are going to need to rely on highly trained small teams for the initial, dangerous construction work and that could easily clash with later social considerations.
I'd honestly give this one over to the military. Give the Pentagon or DARPA a sizeable budget and tell them to develop tools to air-drop a self-constructing base in the middle of hostile conditions (starting desert and Antarctic) an entire command staff and platoon of troops can be deployed into with no prep time. Take that technology and develop it to work in hard vacuum. The secondary benefits here would be substantial so may as well have it work both ways.
Summary;
Technologically, I think most of these are mid-to-short-term solvable problems, meaning you could have solutions by or around 2020. Except maybe the food problem, but I don't know that that's so much solvable. Some areas will just depend on brute force to reach the sort of reliability we need while others are just going to need deep redundancy to make up for the reliability they will lack.
But even saying all this I wouldn't feel comfortable actually implementing this technology in that time frame. 2020 would be when it's all there. I would then want a decade to actually prime it. Run every experiment and test under every set of conditions I can imagine. Have a self-contained biosphere live for five years only with the food we already know could be grown on the moon while releasing random strains of bacteria into their population every few weeks. Make a house-sized facility stand up to hard vacuum for a year without maintenance and with a troupe of chimpanzees running free inside it, fed through a constantly cycling airlock. Use our rockets to run a proof-of-concept project, putting together a remotely constructed, highly complex deep space telescope array.
A moon shot like this is going to be incredibly complex and risky. The technological problems are the easy and obvious ones. We owe it to ourselves to do this right, and that means taking every possible step to minimise the risk and maximise the odds of success. This is an area where there really is no overkill.