Apparently Ann has a piece pf glass lodged in her optic nerve behind one of her eyes and the show implies she is blind, but she would not be blind in her other eye. This means she would have monocular vision.
Superman takes Ann around the world in, what is stated to be, about two hours. Everywhere they go, it's day time, which is an impossibility.
As Superman flies Ann around the world, she is obviously not dressed for cold weather as he flies her over the Himalayas and she has no supplemental oxygen to breathe.
In order for a piece of glass to be lodged in the optic nerve it would have had to pass through the cornea, the lens, and the vitreous first but there is no mention of this making it highly unlikely.
Jimmy Olson states that Superman and Ann will be gone about two hours. Since this is nearly a 25,000 miles trip, that means they would both be traveling at near 12,000 miles per hour. There is no way Ann could breathe or even survive the trip.