In the Land of Legend, the Old King says that he will give two signs of kingship to Abu the thief. Abu is then given three items: a magic crossbow, a quiver, and a small, ornate box, like a jewelry box. No mention is made in the dialogue of this box, but it can be seen in Abu's right hand as he talks to the Old King, and also on the flying carpet as Abu flies away to rescue his friends. Apparently the crossbow and quiver were only one, not two, of the Old King's signs of kingship, and the other sign was the mysterious box, whose magical powers and purpose were lost on the cutting room floor.
At the end, when Ahmad is fighting the palace guards, one of his sword blades is snapped off at the handle, and he stands there without a weapon. After a brief cut, he is running on upward toward the princess and has a good sword in hand again, even though he has neither picked one up off the ground or wrested one from another guard.
The Sultan of Basra's palace has many decorations in the form of Hindu iconography, which would be found in India, but not in the ancient Middle East. (It was considered "Oriental" enough to pass by a 1940s audience, but stands out for a modern audience.)
When Jaffar captures Ahmad and the Princess near the end, he announces "Tomorrow morning they will die the death of a thousand cuts", yet the next morning, only Ahmad is about to be executed, and instead of dying the death of a thousand cuts, he is about to be beheaded.
The wires used to suspend the flying carpet are visible in the last scene of Abu on the carpet. The film was originally shot in three strip Technicolor, with prints made using a dye transfer process that resulted in a slight reduction in overall resolution. This reduction in resolution hid the wires in original prints, making them invisible. Modern prints, especially on Hi-Def DVDs, have restored the resolution making the support wires plainly visible.