Revealing mistake: When the kids are playing around with the plane and make it move along the grass field, tracks from previous takes are visible in front of the plane. When the angle changes the tracks are gone.
Other mistake: Both of the main characters (Affleck and Hartnett) were promoted to captain when they reported to Doolittle. Nearly 1 1/2 months later on board the carrier they still both have LT bars.
Revealing mistake: After Danny's plane crash lands in China, and Rafe runs towards the crash site, he shoots a Japanese soldier. After his next to last shot, the slide locks back on his pistol, indicating it is empty. You can see the slide locked back moments before he takes his last shot, with an empty gun.
Other mistake: When Doolittle's copilot is crossing himself right before take off, his hat has captain's bars on it, but his flight jacket has lieutenant bars on it.
Continuity mistake: When launching Doolittle's plane from the carrier the deck is smooth. When Rafe's plane launches the deck has catapults. The following planes are back to smooth decks with no catapults.
Continuity mistake: When Danny and Evelyn are starting to make love, Evelyn touches Danny's chest and after it she pulls her hand back and grabs his necklace (and dog-tag) way too fast.
Continuity mistake: When Doolittle's raiders are first starting to practice short takeoffs, the flaps of the planes aren't extended in close ups but would have to be for takeoff especially short takeoffs. Planes shown taking off have the flaps extended. In the real takeoff from The Hornet, One pilot retracted his flaps because prop wash from previous planes was lifting his plane. He then forgot about it and took off without flaps extended and was only saved by the heavy wind and forward speed of the carrier. There is actual video of the plane nearly hitting the ocean.
Visible crew/equipment: When Rafe is pouring champagne (after the cork has crashed against his nose) stage lights are reflected on the glasses.
Answer: He is in the scene where the smaller air-base is being attacked by the Japanese. You have to look really closely but he is the driver of one of the jeeps right before the Japanese bomb drops (the one that seems to be a dud and then explodes). Also, Matt seems to be one of the gunners on one of the first ships at Pearl Harbor to return fire (this is not verified but in slo-mo, one of the gunners seems to be him).