What social political and technological problems did the Aztecs face?

SOCIAL: they had to feed the people, a huge city population of about 350,000 people.

That means they had to be farming all the time. They also needed a lot of fresh water which they piped in from fresh springs through aqueducts. The Emperor was in charge of taking care of the people. He was also the top priest and military commander.

POLITICAL: they had conquered most of their rivals, but they still had rivals on both sides of them. On the East they faced the kingdom of Tlaxcalla (who later helped the Spaniards conquer the Aztecs). On the West, they had the Tarascan (Purepecha) kingdom which had already defeated the Aztecs in a battle.

TECHNOLOGICAL: even though they had the technology of the wheel, they did not have any big animals like horses or oxen to pull anything around. So they had to move everything themselves, by human muscle alone.

They also did not have any serious Metallurgy (they used metals like gold for jewelry), so they had no real metal tools. All of their wonderful achievements were done with stones and very sharp volcanic glass called OBSIDIAN.