Visible crew/equipment: In the "Desert of the Real" scene where Morpheus is sitting on the chair while explaining the Matrix to Neo, at a certain point he raises the head to the sky and in that moment the boom mic is visible reflected on his sunglasses.
Visible crew/equipment: In the final scene where Neo exits from the phone booth and wears his sunglasses some crewmembers are reflected on them.
Continuity mistake: When Neo is following Morpheus' instruction to escape the agents who have come to arrest him at work, the location of the knot in his tie changes - note the pattern.
Continuity mistake: In the subway fight scene, Neo is thrown to the floor and wipes blood from his mouth on his hand. It then cuts back to Agent Smith. When it cuts back to Neo, he assumes a fighting stance and you can see that there is no blood on either side of his hands.
Other mistake: The date of birth shown in Neo's passport is 13th September 1971. The date of birth shown in his security file is 11th March 1962.
Continuity mistake: In the "Deja vu" scene, Neo uses a CZ99 pistol to shoot through the wall at the police officer, but when Agent Smith bursts through the wall and grabs him, Neo is holding a Glock 17.
Chosen answer: The pills are the Matrix representations of computer programs. The red pill contains code designed to disrupt Neo's input/output signals, so that Morpheus' team can pinpoint his physical location in the real world. Once located, a signal of unspecified type is sent from their ship, which presumably serves to wake Neo up.
Tailkinker ★