Sidon Ithano, aka the Crimson Corsair, from The Force Awakens proved popular enough from the film to earn his own level.
FN-2199 (A.K.A That Stormtrooper who shouted 'TRAITOR!'and then gave Finn a good walloping with his shock baton) was popular enough to have been given his own miniboss battle and can be unlocked as a playable character in Free Play, despite only having enough screen time to amount to just under a minute.
FN-2199note AKA TR-8R is a tough boss fight, in line with his Memetic Badass fan reputation.
Bragging Rights Reward: Getting 249 Gold Bricks unlocks the Starkiller Destruction special level, the completion of which unlocks the second Death Star as a vehicle in both space levels and as a micro-fighter. Since getting that in the base-game involved doing everything else, and even with the 12 extra bricks through DLC you'll likely have already completed all the levels and side-missions that use vehicles with just a few regular missions and Gold Bricks left, you'll have no reason to use it beyond trying it out for a little bit before finishing up the game.
Can't Use Stairs: While already present for protocol droids like C-3PO, this trope really comes into play for the DLC "The Phantom Limb", as the entire team is composed of regular droid types that can't jump in any way, meaning a large portion of the level involves creating paths for the crew to cross.
Deadpan Snarker: Now that the characters are voiced, some of their lines are more witty than their film counterparts.
Han Solo:[confronting a flametrooper] I guess none of us are secretly fireproof.
Flametrooper 1: A cake?! Let me light the candles! Flametrooper 2: No, wait! That's not a normal cake! Flametrooper 1: I know! It's a huge cake! [Flametrooper 1 lights the candles and the dynamite fuse, blowing him and a couple of others to pieces] Han Solo: Looks like I got my wish after all.
Rey:[towards BB-8, after freeing him from Teedo and getting herself trapped among a Star Destroyer and other Imperial junk] Yeah, I bet you're helping. You're the one who got me here in the first place.
Dwindling Party: Thanks to all the others being Doomed by Canon, the robot crew accompanying C-3PO in "The Phantom Limb" DLC get taken out over the course of the level, until just him and O-MR1 are left, only for O-MR1 to perform a Heroic Sacrifice by walking through acid rain to call for Resistance help, both rendering Threepio the Sole Survivor and leaving his rusted red arm behind as a Tragic Keepsake replacement for the one Threepio lost.
Easter Egg: Combined with Developer's Foresight. There are multiple missions in the open world that first require a protocol droid to translate for an alien citizen to learn what kind of quest they want you to do. Since this is the first voice-acted game in the series and there are multiple protocol droid characters in the game, each one had to have scripted dialogue for the translations because any could have been used. The nature of the dialogue is different for each droid and missionnote O-MR1 is a lot snarkier than C-3PO or PZ-4CO, for example though, and it is impossible to replay the quests on the same file, so each of the droids' scripts you didn't see can become an Easter egg to find on another playthrough.
The Faceless: Captain Phasma. Even when she encounters a Dianoga who stole her helmet after she's thrown into garbage chute, she still manages to cover her head with a bucket, becoming a literal buckethead, until she shoots the Dianoga and steals her helmet back.
Fanboy: The game turns Kylo Ren into a literal Darth Vader fanboy. Everything in his bedroom, and we do mean everything, has Vader's visage plastered over it. He even has Vader slippers at one point!
Imperial Stormtrooper Marksmanship Academy: While there are plenty of jokes from the Stormtroopers about their terrible aim, the necessity of challenge in gameplay means normally they can actually hit you with their shots if you don't dodge or deflect. That said, this game features an "Imperial Inaccuracy" Extra which invokes the idea by making all ranged enemies miss every shot aimed at the player even if you deliberately try to get hit.
Mundane Utility: Palpatine's threatening and evil Force lightning can also be used to... charge switches in lieu of a BB unit.
Nap-Inducing Speak: One Stormtrooper apparently finds General Hux's maniacal speech to be boring enough to fall asleep to, and a fellow trooper wakes him and punches him for it.
Precision F-Strike: The game surprisingly retains the audio of Finn's "one hell of a pilot" line from the movie.
Samus Is a Girl: The First Order has a lot of female stormtroopers, though you can only tell by their voices. Or their heads, if you manage to knock one of their helmets off.
Self-Deprecation: In a flashback to Return of the Jedi, the scene where Luke unmasks Vader is parodied by having his face revealed to be that of Hayden Christensen. Luke panics and quickly swaps his head with that of Vader's actual head. The scene is an obvious jab at the infamous addition of Hayden to the ending of Return of the Jedi in the 2004 DVD and subsequent 2011 Blu-ray.
Suddenly Voiced: While previous LEGO adaptation games had already given characters voices, this still counts as the first of the LEGO Star Wars series to do so. This includes characters that had appeared in past games in the series.
Take Cover!: One of the new mechanics in this game are sections where you need to hide behind chest high walls, or walls that you stand behind, and engage enemies with cover based shooting. It gets changed up every so often, like for instance when instead of shooting enemies you need to throw a bomb at a silver object to make it explode and take something out.
Even when including DLC, BB-8 is the only character capable of using ball switches. This isn't too bad since you get him after Chapter 1, but that still means you can't 100% the DLC or prologue levels as soon as you reach the first hub. There's also the fact that BB-8 has no real use besides that ability which can't be done better by other characters.
Admiral Ackbar's two versions are the only characters which can use water pools to get special items. (Unless you get the DLC packs including Kit Fisto or Jar Jar Binks.)
Some racing challenges on the open world require certain characters or vehicles to play them.
Tickle Torture: The First Order used motorized feather twirlers to tickle their prisoners into giving information, replacing the Cold-Blooded Torture and screams with tickling and laughter.
Turbine Blender: Working on an engine in the D'Qar open world will activate it and suck several GNK droids through it. This will get you a gold brick.
Cereal.
Memetic Badass fan reputation.