Twilight's "fight" with Dr. Milligan. She offers him one chance to put down his gun, as was the custom of her Equine ancestors. When he tries to shoot her, figuring that she doesn't have any of her magic outside the simulation, the bullets are blocked by a biotic field, revealing that even in the real world, she's still a powerful biotic. She then picks him up and starts throwing him around like a rag doll before delivering a biotically-charged kick that sends him flying through a guard rail and into the Harmony Core. This is why you don't mess with Equestrians.
To deal with the four krogan delinquents loitering in New Ponyville, Twilight encourages them to leave by lifting a shipping crate (which is noted as weighing over two TONS) with her biotics, then crushing it like a soda can. Their leader is so intimidated that he agrees to leave without a fight. And just to make sure they don't make any trouble in the future, Twilight says that she'll be happy to repeat her demonstration for any other troublemakers, only next time she would ask for volunteers.
Lt. Pyres' Batman Gambit to keep Applejack out of prison for abducting Dr. Hern from the hospital. He tells her husband that the process of extraditing Applejack from New Ponyville's authority to the Citadel's is expected to take eight months, and that Patricia will need to be kept on the station until the trial. Wanting to get his wife back to Earth as soon as possible, Joshua Hern very reluctantly agrees to drop the charges, only to find out after doing so that the C-Sec medic checking Patricia's condition has declared her unfit for interstellar travel in her condition, and that the determination of a C-Sec officer is not superseded by the order which allowed him to remove her from Huerta Memorial in the first place. And the kicker after the Herns are taken away is that Twilight and Pyres reveal that there is no need for extradition from New Ponyville. The Herd are guests of the Citadel, not a sovereign government, meaning that Pyres was lying through his mandibles in order to protect both Applejack and Patricia.