The two MIBs actually have names. The name of the short, Asian MIB is Lin Sui-Xi. The name of the tall, Caucasian MIB is Karl Haushofer. His character was the only one to be addressed by name during the series.
There are numerous references to Macintosh and Apple Computers: The phrase "To Be Continued", with a colored "Be" is shown at the end of most of the episodes. This is a reference to BeOS, whose logo has similar coloring. The Be company was founded by Jean-Louis Guasse, a former Apple executive. The Navis use an operating system named Copeland, which was the codename for Apple's MacOS 8. Navi's operating system has a graphical user interface (GUI) similar to that of MacOS. Arisu's Navi resembles the original Apple iMac. The series slogan "Close this world. Open the NeXT" is a reference to the NeXT company, founded by Steve Jobs in the late '80s and purchased by Apple Computer in December 1996. All of the Navis shown in the series use one-button mice as Macintosh computers do. The electronic voice heard saying the episode titles is the "Whisper" voice from the MacOS Speech Control Panel, a program that permits text-to-speech. The child's Navi that Lain used to use was modeled after the 20th Anniversary Macintosh. The HandiNAVI, the handheld computers which both Lain and Arisu used was based off the Apple Newton, the first PDA. Navis and Macintoshes are both built by companies named after fruit, Tachibana (a type of orange) and Apple, respectively.
In Layer:04, the boy playing Phantoma asks Lain if she's a PK. A PK is a "player killer", a term originating from the early days of online MUD (Multi User Dungeon) games. A PK is a player who kills other players.
The Psyche processor is pronounced as "psukhe", the original Greek form of the word.
The girl in the "Devices" segments is the voice of Lain herself, Kaori Shimizu. Also, Lain's character design was based in part from Ms. Shimizu's physical appearance.