The fact that Charles of the past is close to tears or in some miserable state for almost the entirety of the movie. Seeing those wide, hopeful blue eyes so tearful and defeated is absolutely gut-wrenching.
As Xavier explains to the future mutants about Mystique, he regretfully mentions that he'd tried to help her but only succeeded in "pushing her away." If you look closely at Magneto, despite remaining perfectly still, there seems to be a definite look of sadness, if not shame, on his face. Now remember what he did to her in The Last Stand.
Mystique finding the autopsy reports at Trask Industries, and seeing the pictures of Angel and Azazel's bodies, among others. It only adds fuel to her hatred for Trask.
She lets out a tiny, pained gasp when turning one page over; turns out that's the page showing Angel's body. Seeing her co-workers is bad enough, but then she starts seeing her friends...
If Movie!Nightcrawler is still Mystique's son with Azazel, then it means she just saw the body of her lover and father of her child being used in scientific research.
Pay close attention and you'll notice that Azazel's autopsy photos are what are shown right before she really starts to lose her composure. Even if he was only an fb that she happened to be impregnated by, it's still got to be painful to see him like that.
Also, even though the bad timeline of the future gets erased because Logan's mission ends up being successful, those mutants are still dead in the bad timeline, because Logan arrived in the past only after they were killed already.
Seeing the Future Sentinels slaughter the X-Men one by one.
You have to watch this twice; once in the opening and again during the climax.
It's even more brutal the second time because the first time, they die relatively quick. The second time feels like a last stand because they know that, one way or another, their existence will be wiped out. Should Wolverine succeed, they will cease to exist with their timeline. Should Logan fail, no one will be able to come back, which means this will be their true death with no reset. So they fight with every last bit they had and end up dying horrific deaths.
During the final battle, Kitty's look of absolute, tear-stained despair after seeing Bobby, whom she's hinted to be in a romantic relationship with, die horribly while making the last stand to protect her and the others left inside.
Kitty in general by the end. Picture this: she is constantly in excruciating pain, to the point that she is in tears, from when Logan accidentally cut her and is slowly bleeding out. Meanwhile she has to keep fighting through the pain and stay focused on Logan and keeping him in the past, or she may cause an even worse future for her kind, all the while knowing that all of her remaining friends, including aforementioned Implied Love Interest Bobby, are fighting a hopeless battle that will unquestionably end in their horrible deaths, including the Professor.
The worst part is this happens over Magneto's New Era Speech. This is the future he's ushering in for his people.
Storm's death hits the hardest. The music and the reactions from Professor X and the rest of the X-Men sell it as a tremendous tragedy, and it makes her death feel like it has a lot of weight to it.
Magneto almost managing to stop the Sentinels, then looking slowly downward after the explosions cease... and pulling a shard of shrapnel from his chest, the tip visibly soaked in blood. He doesn't even flee after that, using scraps of metal to reinforce the entrance behind him, fully willing to die out there, and he probably would have, had he not been pulled to "safety" by Kitty and Blink, so he instead gets to slowly bleed out inside the stronghold.
When we first see Young!Xavier, it's quite funny, as he looks like your average hippy. He's all goofed-out and clearly doing some form of drugs; plus, he's walking again! As the conversation goes on, it quickly becomes a lot less laughable. Then Hank explains to Logan what happened to the leader of the X-Men, how losing his sister, best friend, students and teachers left him almost completely alone, with only Hank and his powers (which spiraled out of control the worse his emotional state got). Hank designed a serum to both help Xavier walk and to stop his powers from working. It is truly heartrending to see Young!Xavier self-medicate with syringe after syringe to stop the voices in his head. It's even worse if you've ever known drug addicts.
Erik: You sacrificed your powers so that you could walk? Charles: I sacrificed my powers so that I could sleep.
For fans of the comic books, it's even more tragic watching Charles frequently drown his sorrows because his mother Sharon became an alcoholic not long after her first husband died. It's hinted in First Class that she was an emotionally negligent parent, and while Charles' personality is very different from hers, he nevertheless inherited her self-destructive coping mechanism when dealing with profound loss.
It's painful any time Erik or Mystique ask Charles to use his powers to help/protect them, only for Charles to shakily admit that he can't.
During one point in the film, when Logan, Hank, and Charles are coming back to the school, Charles begins to collapse from the agony of Hank's drugs wearing off. He begins crying out in pain that the voices are coming back and begs Hank to "make them stop."
Worse, Charles pressing the needle of the syringe with the serum in it against his arm, conflicted and sobbing, before finally deciding to try and help again, slamming the needle down and burying his face in his hands.
Erik lashing out at Charles, mentioning how so many of the cast of First Class suffered a Bus Crash. Although most of the mutants were either enemies or betrayers of Xavier whose deaths he likely won't mourn, it's Sean Cassidy's name (Banshee) that really hits home. It's the only one that pulls a visible and heartbreaking reaction from Charles.
Then, when Erik nearly crashes the plane and he regains control of himself, Charles gives him a look of disgust before storming up to the cockpit. There's a small amount of regret on Erik's face at what he just said.
Before Erik unleashes his fury at his former friend, he reminds Charles that he's lost his fair share. Charles just scoffs and tells him to dry his eyes. For Charles, who's been inside his mind to so utterly disrespect and snark at the trauma and the loss he knows Erik suffered during the Holocaust and more is heartbreaking and shows the gulf that's developed between them.
The moment when Mystique is finally pointing a gun at Trask and Xavier gets into her head one last time to convince her not to do it and the subsequent montage of the faces of the mutants whose fates rest in her hands.
The scene between the two Charleses, future and past, as Future!Charles tries to comfort and inspire his younger self, with the sort of quiet dignity and gentle wisdom that only Patrick Stewart can deliver, and reminds us just why Xavier is the heart and soul of the X-Men.
Future!Charles: Its not their pain youre afraid of; it's yours, Charles. And frightening as it may be, their pain will make you stronger, if you allow yourself to feel it. Embrace it. It will make you more powerful than you ever imagined. It's the greatest gift we have that can bear pain without breaking, and it's born from the most human power—hope. Please, Charles. We need you to hope again.
Erik coming to the conclusion that he has to kill Mystique to prevent the Bad Future from occurring. Michael Fassbender's conveying of Erik's deep personal conflict both when he first comes to this realization and as he's preparing to shoot her after she tries to escape really brings home the sting. Not to mention Mystique's look of confusion and despair when he first points the gun at her.
Magneto's lament to Xavier as the former lays dying.
The 25 moments viral site reveals several events in mutant history in the original trilogy/Bad Future timeline, including the fates of some of the original characters after The Last Stand. Kitty Pryde is imprisoned in a mutant internment camp and subjected to a power inhibition collar created by Trask Industries, Angel is killed by Sentinels during an Occupy protest, and Beast is brutally murdered outside his home by an anti-mutant group (especially horrific because, as the site points out, he was "the mutant most famous for successfully integrating with human population"). The accompanying image for the latter event shows Magneto standing at his grave.
When Past!Charles is attempting to convince Mystique to stop her mission of killing Trask at the airport, he uses multiple people to speak through to try and communicate with her before he is able to make an apparition of himself. Despite attempting desperately to plead with her and change her mind, she ends up rebuffing him and literally walks through him.
After Logan's memories of Stryker are triggered by the man twitching on the ground before him, his past self temporarily resurfaces. After he regains stability, Charles asks him what's wrong after Logan watches Stryker get away. Logan is one of the toughest characters in the series, but his future self almost collapses in panic and his past self acts scared.
Logan: I just saw somebody who's going to bring me a lot of pain someday.
The Paris sequence is a pile-up of Tear Jerkers. Logan is having a panic attack, Erik is trying to kill Mystique, and Charles is powerless to stop any of it. To top it all off, the sequence ends with Hank, in full-on Beast mode, displayed in front of dozens of terrified civilians like some kind of freak show. Keep in mind that this was the guy who was desperate to appear normal even back when his only problem was "weird feet." Now he's a snarling, furry blue monster and everyone can see him.
When they meet again immediately afterwards, Erik tells Raven what he knows about the future. At first, she doesn't believe him, and he tells her that killing Trask won't be enough. It's clear how poisonous Erik's influence on Raven actually is, the only man who ever complimented her beauty is the same man pushing her towards murder.
Erik: Killing one man isn't enough. Raven: ...It never was for you.
After that, Raven promptly leaves and Erik looks around, trying to find her, a grief-stricken look on his face.
Seeing Past!Charles try and use Cerebro for the first time in a decade is harsh. After years of closing these same voices out, he is suddenly bombarded with the rush of thousands of people's emotions—including agonized screams of sorrow and pain, either from their own personal lives, or Charles trying too hard to focus in the machine and hurting them. Charles is easily overwhelmed and in tears by the end of it.
As Past!Charles looks into Logan's mind, he sees images of Logan's lifetime, which include his being part of the Weapon X program, his love for Jean, and ultimately having to kill her as Dark Phoenix. Despite all his pain, misery, depression, Past!Charles' reaction is both devastated and horrified - which says it all, really:
Past!Charles: (voice trembling) You poor, poor man. Wolverine: Look past me. Past!Charles: No, no, I don't want your suffering, I DON'T WANT YOUR FUTURE!!!
When Trask is analyzing the bit of blood they got from Mystique, he turns around, looks at a young Colonel Stryker, and asks about his son.
Past!Stryker: Oh, Jason? He just turned ten, sir.
Ironically enough, Stryker gets another surprisingly humanizing moment a second later. When Trask asks him how many men were lost in the Vietnam War, Stryker takes a moment to look down at his feet in genuine grief. Seems he did have the capacity to care, once.
Hank asks Logan if he makes it in the future, and Logan bluntly replies that he doesn't, but adds that they can change that. Put in the context of their friendship, and Logan teasing him earlier to get him to reveal the Beast within him, and the current situation they're in, it comes across as Logan desperately trying to convince Hank and himself that they can still change the future.
Overlaps with meta-example: When Charles said that Raven's heart belongs to somebody else now, we are shown a glimpse of a saddened Hank. Jennifer Lawrence and Nicholas Hoult once dated, but now they are separated.
Although it may be very subtle, the moment Magneto lands in the RFK Stadium and the custodian asks if he can help him (out of confusion for appearing suddenly), Erik simply replies "No...you can't". At that point in his life, Erik can't look back on his actions and has to be Magneto before attacking the White House.
The Rogue Cut
Seeing the damaged Xavier mansion under the control of the "worst of humanity" Logan talked about in the Bad Future, and it's then swiftly consumed by flames during the X-Men's escape as a sorrowful Charles watches from the jet.
Everything to do with Rogue. She spends an unknown amount of time being experimented on in what was once her home, her former boyfriend dies horribly rescuing her, and just a few hours later, the Sentinels kill what's left of her friends, and march on her. Anna Paquin's acting, slowly breaking down into tears as the Sentinels break through the door, really sells the scene.
Speaking of ex-boyfriends... In X-Men: The Last Stand, Rogue saw Bobby become overly friendly to Kitty (the ice rink scene), and now Bobby and Kitty are in a relationship. This would imply that he began a romance with Kitty after Rogue went missing despite his strong suspicion that Rogue was being experimented on by Trask Industries in the X-Mansion's former Cerebro room (which blocks telepathy). This might explain the cold look Rogue gave to Kitty just before she stole the latter's powers.
Bobby is killed earlier than in the theatrical version when he rescues Rogue, who is unable to help him because she's barely recovered from the experiments done on her. Bobby and Kitty are actually revealed to be in a relationship, and she begs him to bring himself safely back as well. The look Rogue gives Kitty when she asks where Bobby is says it all, and Kitty absolutely breaks down crying upon hearing the news. To rub more salt into the wound, Rogue has to steal Kitty's power right then so she can take over projecting Logan into the past, adding more (and physical) pain for Kitty to endure in her grief.
There is an added scene with the younger Charles at the Sentinel demonstration, where the crippled soldier next to him chats him up, asking how he lost the use of his legs. Charles pauses before responding "friendly fire." Ouch.
The added romance scene between Mystique and Beast has her reminding him that some time ago he told her that their natural appearances would "never be considered beautiful", and it's obvious how much that still hurts her. Beast clearly regrets saying that, and sincerely tells her now her natural blue form is beautiful to him... but when she asks whether he can also see himself as beautiful, he can't reply, and any chance of a relationship between him and the "mutant, and proud" Mystique fails because, even years later, he is still ashamed of what he looks like.