Easter egg: To see a mini documentary on 360 effects, go to the dream world menu and look for a red pill. Highlight it and press enter.
Easter egg: A montage can be found in the Special features menu. In the cast and crew bios the page on the writing directing Wachowski Brothers contains a small red pill. Select the pill to see a twelve minute montage of concept art and special effects test footage.
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 ★