Beacon of Gondor
In the mission Test Flight, part of the chapter Friends in High Places, a beacon can be spotted on the top of one of the mountains. Successfully hitting the beacon with a rocket will make it ignite and burst into flames. All other beacons encountered subsequently will also be on fire. This is probably a reference to a scene from the film The Lord of the Rings: The Return of the King.
We Love DICE Los Angeles
In the mission Cape Helles, part of the chapter The Runner, there are 20 flags hanging on the dreadnought ship. Using the International Code of Signals, they translate to We Love DICE Los Angeles. DICE LA is one of the EA DICE studios working on Battlefield 1.
Show Me the Way to Go Home
In the mission Steel on Steel, part of the chapter Through Mud and Blood, once you've successfully defeated the final incoming attack wave, the landship crew will start singing the song "Show me the way to go home" if the landship stops moving. This song was also used in the film Jaws.