EIGHT WHEELS ON MY WAGON
At the start of mission 4 (No Hope in Hadley's) you encounter several vehicles on the path to the colony. The first is a stranded 8-wheeled Daihotai Tractor, which is seen in the special edition of Aliens being driven by Newt's family as they go to investigate the The Derelict. The second vehicle is an M577 Armoured Personnel Carrier, as driven by Ripley in the film.
When you reach the colony itself, you can see a faithful recreation of the Hadley's Hope (pop. 158) sign amongst the wreckage, complete with the "Have a nice day!" graffiti across the top.
I WANT TO RIDE MY TRICYCLE
There are a couple of locations in the game where you can find a Weyland-Yutani branded low-slung tricycle. The first one is in the hidden Easter egg room mentioned previously, and the second is in a side room to the left of the corridor after you enter Hadley's Hope in mission 4.
This tricycle is seen near the beginning of the special edition, when a child is told off for racing it down a corridor onboard Gateway Station. A similar tricycle can be seen in The Terminator, which was also directed by James Cameron.
After entering Hadley's Hope for the first time, go to the side room on the left of the corridor (where the tricycle is) and listen to the audio log. The voice is Ann Jorden (Newt's mother) relaying events seen in the special edition, where her husband Russ is implanted by a facehugger while investigating The Derelict.
Towards the end of the recording you hear Newt herself speak, saying her father is waiting for them in the cafeteria. As he was implanted with a chestburster at this point, this is most likely the source of the Xenomorph infestation that wiped out the colony.
As you move on through Hadley's you pick up something on your motion tracker, though after investigation this turns out to be a false positive of "somebody's lost blanket" hanging down from a ceiling fan. As Newt was hiding in the air ducts this almost certainly belongs to her.
While exploring Hadley's Hope you'll come across two sentry turrets protecting a corridor, one of which is completely out of ammo and the other is down to the final few bullets. These are seen in the special edition of the film, where a xenomorph attack is thwarted by the guns moments before their munitions supply runs out.
The ammo count displayed on the sentry turrets is meant to correspond with the film, however the readouts in the game show 04 and 000 whereas in the film the amounts are actually 010 and 000 - perhaps a few more bullets were fired before you arrived...