The two puppets dangling from Screaming Mantis appear to be Psycho Mantis and The Sorrow from previous Metal Gear Solid games.
During the Nomad briefing missions, take control of the Mk II and go to the right of the helicopter. There are three separately caged chickens, each with its own label: "Solid", "Liquid", and "Solidus"--a reference to the three Big Boss clones. A further reference to those chickens happens at the start of Act 1 when Sunny is cooking eggs. She says "Only two eggs? Solidus must've taken the day off."
When Snake and Naomi talk about war changing and how it used to be "just a game", all of the Metal Gear Solid titles appear in an indexed list. After Metal Gear Solid 4, there are a couple boxes titled "In Production.
Otacon has a model of Rex next to his computer.
The rubber duck in the upper gantry of the Nomad can also be found in Capture The Flag mode in Metal Gear Online; in the GA-KO camouflage in Metal Gear Solid 3; and can be found floating in the flooded Shell Core in Metal Gear Solid 2.
When you first enter Big Mama's hideout and the guards talk about Snake, press L1 to see posters from Metal Gear Solid, Metal Gear Solid 2, Metal Gear Solid 3, and Metal Gear Solid: Portable Ops.
During the final showdown with Liquid, when it enters the third stage of the fight, Liquid will do Ocelot's signature hand gesture.