What are the main issues that are preventing a human mission to Mars? Is it just because it'd be very expensive?
Or are there serious problems that need to be dealt with, studied and solved? If so, what are they?
 A: Money certainly is one issue, but it is far from the only issue. It isn't even the biggest issue.
Issue #1: Humans need air, water, and food.
We can live without air for a few seconds, without water for a few hours, without food for a few days. And then we die. We need air, water, and food. And we don't know how to do that on Mars.
There are conjectures that various chemical processes can be used to liberate oxygen from the Martian regolith or Martian atmosphere. These are but conjectures. Taking a conjecture (technology readiness level 1) to something that can reliably be used to support human life (technology readiness level 9) is not an easy process. Generating oxygen is quite feasible, but reliability is a different matter.
Water is even tougher nut to crack than is air. Food? What we do know is that every attempt to make a self-sustaining environment has failed miserably.
Basically, we don't know how to do that.
Issue #2: Humans need to come home.
Given the above, sending humans to Mars permanently would be murder. We haven't the foggiest idea how to send humans on a permanent basis. Until we solve the problems of air, water, and food, we need to bring our explorers home. This represents an exponential increase in cost.
This means sending a launch-capable lander to the surface. The biggest thing we've sent to the surface of Mars is the 900 kilogram Curiosity rover. A launch-capable lander would necessarily be many orders of magnitude larger. Crossing multiple orders of magnitude in physics is easy. In engineering, it's not so easy.
Basically, we don't know how to do that. 
Issue #3: Precision landing.
The Mars One concept shows multiple vehicles, side by side, on the surface of Mars. That is pure science fiction.
Because of issue #1, we'll need to send lots of supplies to the Martian explorers, enough to last the hundreds of days that orbital mechanics says they will have to stay on Mars before coming home. The amount needed is staggering, much more than can be carried on a single lander. That means multiple vehicles landing on Mars, all carrying supplies needed by explorers. They'll need to land close enough to one another that our intrepid Mars explorers could conceivably make a foray to and retrieve those resources.
There's one minor problem here: This is yet another "we don't know how to do that" kind of problem. The current concept of "precision landing" on Mars means not missing the target by hundreds of kilometers.
Basically, we don't know how to do that.
Issue #4: Humans can be stupid and crazy.
This is perhaps the hardest nut to crack. The premise behind Mars One is that it will be a highly-watched reality TV show. The kinds of people that make a reality TV show garner big ratings are exactly the kinds of people we absolutely do not want to send to Mars. Various navies of the world have studied the personality traits of people who do well on long, isolated assignments in submarines. Needless to say, these are not the drama kings and drama queens that make reality TV so entertaining.
The shortest round trip to Mars will be over two years long. That's too much time for even the most stable of personalities.
Addendum
I recently left working for NASA after over a three decade long career there. (I hope I still have another decade to go, but elsewhere.) I worked with people who studied the Mars problem. The next good opportunity to send people to Mars is only a few years away. That's too short. The opportunity after that occurs in 2035. The twenty years between now and then might well provide enough time to change "we don't know how to do that" into "we absolutely can do that".
A: There is another problem here. How to shield humans from the hard radiation (high energy protons and neutrons) from the Sun and Galactic cosmic ray sources, once outside the Earth's magnetosphere. 
Analysis of data from instruments on board the Mars Curiosity spacecraft and on the Rover itself, allowed Zeitlin et al. (2014) to compare the equivalent radiation dose (or dose-equivalent rate) and the NASA design reference mission (180 days out, 500 days on the surface and 180 days back) with current health and safety standards.
The outward/inward journey features an equivalent dose rate of 1.8 milli-sieverts/day and then a further 0.64 milli-sieverts/day whilst on the surface. A total dose of 1 sievert (=100 rem) would be experienced (about the same as 2000 medical X-ray investigations)- although it should be noted that the Sun wasn't particularly active during these measurements.
This does not appear to be a show-stopper and presumably some clever shielding options could reduce this a bit. An acute dose of this size would increase cancer risk, it's about 5 times the recommended amount of occupational exposure and about 50 times the average dose received in the USA.
However, it is not clear what would happen if there were bursts of strong solar activity whilst in the cruise phase or on the Martian surface. Some sort of contingency plan would be needed, but it is difficult to shield against the high energy Galactic cosmic rays which would be more prevalent in periods of low solar activity.
