When the soldiers find Darius' chariot, there are dual cutting blades attached to the wheels. Seconds later, when the chariot is driven away, the blades are gone. Not enough time elapsed for the blades to be removed.
The Persian lead chariot turns turtle, and in the next scene (in the 1:45:44 mark) disappears.
When the Macedonian horsemen attack Darius' soldiers, one of the spear tips clearly bends in a way that shows it to be made of rubber.
Many of the actors playing soldiers wear comically ill-fitting helmets, including the star's own. Burton's helmet never sits properly on his head and has fabric stuffed into the empty ear holes in a vain attempt to cover up the gaff. A simple session of "musical-helmets" amongst everyone could have solved the problem quickly and economically.
In the final battle, the Persian lead chariot turns turtle without even being attacked.
Both Alexander and Aristotle are seen with books bound in the modern way. At this time all books were in scroll form.