The opening text is based on obsolete information. The "laws of aviation" from the early 20th century explained the flight of large objects such as airplanes and birds but failed when applied to really small objects like bees. Modern laws of aviation do explain the flight of bees.
(at around 21 mins) When Vanessa has just saved Barry and has him under a glass with Ken's brochure underneath the glass. There is a close up and the word "backwards" can clearly be read although upside down. The shot changes to Vanessa opening the window and letting Barry out. Barry and the glass are now over a photo.
(at around 1h 14 mins) At one point all the trees and plants have withered because of a lack of pollination. But when all the bees fly out to help guide in the plane, the tree in front of the hive is sporting big green leaves.
(at around 36 mins) The windshield-wipers that Barry and the mosquito are riding on, don't move all the way over to the driver's side of the wind-shield. However; the marks made by the wipers do go all the way over to the driver's side of the wind-shield.
Plants don't wither and die if they are not pollinated, they simply don't develop viable seeds. Although bees do contribute significantly to the pollination process, other animals do the same thing, not to mention that a simple gust of wind can cause pollination. Unpollinated plants will simply bloom again at another time, giving another chance for pollination.
Although a large enough swarm of bees could theoretically generate as much lift as a jet liner, the bees would have experienced "vacuum" forces between themselves and the body of the jet at the speeds depicted, rather than generating lift, like two ping-pong balls being drawn together by blowing a stream of air between them.
Adam stings Montgomery and ends up in the hospital still living with a plastic sword as a replacement stinger. In reality, once a bee loses its stinger, the bee dies leaving behind not only its stinger, but part of its abdomen and digestive tracts as well as its muscles and nerves.