The subway sequence echoes an early scene in the film Jacob's Ladder, right down to the name of the street that Jacob is trying to reach.
The unlockable Beam Saber weapon is based on the Laser Blades used by the heroes of the Japanese Space Sheriff superhero shows, Gavan, Sharivan, and Shaider. In particular, the way Heather activates the Beam Saber by drawing her hand along the blade mimics the way the sheriffs would charge their weapons up for their Finishing Moves.
There's a scene in the Dark Office Building where a lone wheelchair is visible from a great distance, illuminated by a single light. Word of God has confirmed this is a shout out to the memorably creepy "Hello...Gordon" scene from "Session 9".
Solid Snake appears as the corpse in the wall of the construction site where you get the silencer. This isn't clear in-game but was confirmed by Konami.
The Borley Haunted Mansion at the amusement park is almost certainly named after, well, the Borley haunted mansion, better known as the Borley Rectory, reputedly the most haunted house in England.