GET A HEAD
When Newt is found in the film, she is clutching a doll's head - one of the few toys she was able to salvage while evading the Xenomorphs by hiding in the air ducts. This item can also be found in the game, while traversing the sewers in mission 5 (The Raven).
After the checkpoint where you turn on a Sewage Pump and the nearby Xenos explode, turn right at the steps down from the platform, then left at the junction ahead and look down a short tunnel on the right to see the doll's head on top of a barrel. Finding it also awards the trophy or achievement 'Mostly Come at Night...', referencing Newt's assertion that "They mostly come at night... mostly."
A SONG AND DANCE
During mission 7 (One Bullet) when you start sneaking into the laboratories, ignore O'Neal and go through the door to your right instead. Head to the far end of this room and you'll find a straw boater and cane sealed in a containment capsule.
This is a nod to the Mel Brooks parody film Spaceballs, in which an alien bursts out of John Hurt's chest (spoofing his role of Kane from the original Alien), then dons a straw boater hat and cane to perform "Hello! Ma Baby" along the diner's bar before scuttling off.
SKY ROCKETS IN FLIGHT
While moving through The Derelict in mission 8 (Rampart) you'll reach the main control room and find the body of a Space Jockey in the centre. Once you've dispatched all the enemies, aim for its head and keeping shooting it there until a holographic recording begins playing.
This looped projection shows The Derelict in a pitched space battle with an unidentified circular ship, which leads to the craft crash-landing on LV-426 and coming to rest at its current location.
BONUS SECRET: DOUGHNUT ADJUST YOUR SET
On mission 7 (One Bullet), after passing through the first building look at the ledge to your right and you'll see a box of doughnuts. Shooting it triggers a giant doughnut rolling down the hill towards you, before exploding in the lava below!