When Jamal is pulled from the moat, his clothes are bone dry.
When Jamal is lying down on his bed after being knocked out, Victoria pulls out his chain to inspect it. When he is stirred by her touch and sits up, the chain is no longer hanging out but is neatly tucked back into his shirt.
Jamal falls into the lake, but the bills he hands the vagrant are not wet.
When Jamal is back at the lake, debating whether it's his fight or not, the medallion is tucked inside his shirt. When he turns to face the camera it's suddenly outside his shirt, and when he turns around again it's back inside.
Jamal rips off his shirt pocket to reveal his logo, but immediately afterwards, the pocket has sewn itself back on again.
The executioner tries to cut a melon with an axe two times before turning the axe blade sideways, and smashing the melon. The force of a blow from the edge of an axe would be greater than from the flat, so if he can't cut the melon, he should not be able to break it with the flat of the axe either.
Jamal asks Victoria about the current date, which he says, "Is it Sunday, the 5th?" And after she confirms, he says "2001?" To which she informs him, much to his shock that it is currently the year 1328 in England. So, assuming given that August was the only month in 2001 to have the 5th day on a Sunday, and that scene took place on August 5, 1328, which was the same date in 2001 when he fell in the lake; then it would be a Friday.
As Jamal prepares for his invasion of the castle at the end of the movie, he's seen testing the way he will "breathe fire" in his Black Knight appearance. He's seen using a Bic style lighter, and an aerosol can to simulate breathing fire. He may have carried a lighter in his pocket back to the 14th century, but he most definitely is not carrying a large aerosol can which wasn't invented until the 20th century.
There are several inaccuracies about 14th-century England in the movie, including the names and ages of the royal family, the English dialect people spoke, and the ethnic makeup of its population. However, this movie is a very loose adaptation of "A Connecticut Yankee in King Arthur's Court" by Mark Twain. This novel was written not as a realistic representation of history, but as a satirical treatise on Western civilization generally.
As the camera pulls back after Jamal falls into the moat and "disappears", he can be seen at the lower right of the screen swimming away.
When Jamal is fighting on top of the castle in his "Black Knight" armor, it bends like the synthetic material it is, and does not remain rigid as metal would.
For the final fight scene when Jamal arrives as The Black Knight, he is breathing fire through his helmet using a lighter and an aerosol can. That would by all human methods require two hands, but he clearly his holding a sword in one hand, and the horse's reigns in the other leaving no way to hold an aerosol can and a lighter.