(at around 16 mins) While learning of the foreclosure from his dad, Billy's bag strap momentarily changes from beneath his shirt collar to atop his shirt collar.
(at 12 mins 48 secs) Billy swims to the shore where Allie is sitting and uses a towel to dry his hair and wrap around his shoulders while they talk. He starts to walk off, still shirtless, but moments later (at 13 mins 41 secs) he is wearing a shirt, carrying a pack with its strap across his shoulder, and with no towel in sight.
(at 14 mins 14 secs) As Billy and Allie ride up to the orphanage on his scooter and pass the orphanage sign, a dark brown pack is in Billy's lap with a narrow tan strap running from his right shoulder to his left hip. The shot cuts to one of the scooter stopping where Billy's lap is empty and a wide, dark canvas strap of a different pack runs from his right shoulder to his left hip.
(at 28 mins 56 secs) When Billy makes his wish in his father's house, the neck of his shirt is buttoned up and the medallion strap is around his neck on top of his shirt. After Billy makes his wish, the neck of his shirt is open and the strap of the medallion is around Billy's neck inside his shirt.
(at around 23 mins) Billy finds King Kiele's medallion wrapped in cloth. Though buried for a few centuries in a tropical jungle environment, the cloth has not deteriorated.
(at around 55 mins) Billy scurries around the warriors' boats yet leaves no footprints or marks in the moist sand (especially from his modern-era waffle-sole boots). With an enemy guard looking directly at the boats, Billy further manages to climb inside one and cover himself with a blanket.
(at around 1h 1 min) Instead of binding the captured boys at the wrists before setting them on a forced march, the warriors build a bulky, complex bamboo cage (wherein the boys can sit comfortably). With the boys inside, they proceed to carry them back to their leader through a bamboo forest. In terms of energy, this has the effect of delaying their return and keeping the boys fresh for action (especially if they were to escape) while tiring out their captors. (Though the warriors' instructions were to retrieve the boys' dead bodies, not bring them back alive and in good condition, this order was based on the assumption they were already dead.)
(at around 1h 8 mins) Allie scares off the warriors with firecrackers, but it's unclear how she had them or how she lit them, since it's doubtful she had either matches or a lighter or firecrackers on her when she fell back through time with Billy.