I should first say that dictatorships can be successful. In the West, we have a decidedly negative view. So, it is important to point out the other side. Now here are some weaknesses.
First, dictatorships are usually based upon force and violence. Therefore, opposition often results in bloodshed. This makes for bitterness and potential rebellion in the future. Moreover, other nations do not look favorably on dictatorships.
Second, since dictatorships are based on fear, the freedom of the people is curtailed. So, the creativity and expressions of the people will not burgeon. This is a big weakness, because many innovative initiatives in science, economics, and technology are driven by people who are free.
Third, there is always the problem of succession. When the dictator grows old and dies, what will happen? If he keeps it in the family, a son may not be able to govern or even want to govern. There is also the possibility of a coup during these transitional times.
Finally, the international community often shuns dictatorships. Sanctions and embargoes can cripple a dictatorship and keep them from flourishing.