I don't know all the details of caliphate either, or if such detailed explanations exists. Removing someone from power. There would have to be some kind of recall voting system, where people can vote him out.
Democracy breads criminals because the laws brought by it are lax. For example, you have pro-death penalty people, and some against it. Those who are against it seem to be winning in the West, and there is rarely death penalty anywhere now days. It's similar with things like child abuse etc, which is currently an issue in the US. Caliphate would bring Sharia which would stamp out most criminals (of course not all).
I would argue that the US is the most advanced country democracy-wise, but even there, there are many things that are unjust, even with all the checks and balances. Look at the war in Iraq and other issues. One half of the country is satisfyed with what is going on and the other isn't . They faked the evidence for war, and where were the check and balances, where is the impeachment for misguiding the people? In my opinion, the people in US are nearly powerless, even though it seems like they have a lot of power. This becomes very apparent in other, less advanced democratic countires. The recent election in Ukraine where the votes were falsified. In the end, the only checks and balaces were the people themselves. The government mechanisms were ineffective. Bosnia is another country were democracy is just not working. Everybody is pulling their own way and nothing gets done. The people in the goverment get the highest pays, but do the least amount of work. And the corruption is all over the place. I don't think democracy is working in Russia either, although I'm not into their politics, so I dont' know for sure.
All in all, I agree that the democracy is the best of the current systems. But I think that it could be easily modified and tranformed into a Caliphate which would have all the benefits of a democratic rule, but swiftness and effectivness of a dictatorship.
The modifications would be abolishment of secularism and certain aspects of capitalism. Also, probably getting rid of parties, as there wouldn't be any key issues around which people would pull together. Forming a council which would advise the Caliph would be a good idea.
Introduction of Sharia as the main constitution. Keeping freedom of press (political freedom, not freedom to draw cartoons of the Prophet (saws)), and freedom of speach, power of recall, providing people with a chance to grow withing the state. These are some of the things that are not part of a dictatorship, which is what makes it so oppressive.
Withing this kind of system, there woulnd't be much of a chance for a lot of unjustice, as Sharia leaves very little room to manuever. The only bad scenario would be if some extremist came to power and introduced redicolous laws aka Taliban. But, in that case, the people would have the power to vote and kick him out.
This is just an outline, there is many other quirks and glitches that would have to be worked out, but this system would be miles ahead of the democracy as it is today.
It would give power to the people, while at the same time increasing the effectivness of the state as a single body.