Breather Level: The brain transplant surgery is significantly easier than the heart and double kidneys transplant surgeries due to having less steps to do, but the difficult controls will still be your major obstacle.
The line gets crossed when you accidentally get the drill stuck in the patient. It gets crossed again while you flail about trying to get it out as it whips around by its drill bit.
This phone call:
Nigel's friend: A'right Nigel, I've been wondering what going on with that mystery meat you've been sellin' me. Half my customers think it's absolutely lovely, the other half have been puking their guts up! Not that I mind, mind you; I just put it back into the kebabs.
It's entirely possible, in the Ambulance Brain Transplant, to have the patient instantly killed by a fire extinguisher to the brain. Less than five seconds in the surgery.
Game Breaker: The experimental mode with the Razer Hydra controller gives you two hands and a lot more dexterity. If it actually worked for every level, the game would be a lot easier than it's supposed to be.
Even more so when played in VR with the HTC Vive. The game's wacky mechanics become practically trivial.
Good Bad Bugs: In Meet the Medic, you can use the Pyro's axe on the Heavy's ribcage, which can break the bones without losing one pint of blood. Of course the only thing that'll be getting in your way is trying to swing it effectively and maneuvering around the controls.
Suspiciously Similar Song: The initial segment of the track "Unidentified Flying Organ" (Which plays during the alien surgery) sounds suspiciously similar to the theme music of the series The X-Files.
Tear Jerker: The music that plays if you fail a surgery.
That One Achievement: There are various achievements that qualify, but here are the ones that take the cake:
"Nothing But Skull". As the description says, you have to throw the replacement brain into the patient's head to finish the brain transplant. What it doesn't tell you is that you have to throw it with your hand pulled all the way back and in an underhand arc. This is a pain to accomplish even if you know how to do it, though you can cheat somewhat by quickly moving your hand to assist after the toss. This is one of the few achievements from the original game ranked as under 1% completed worldwide, and with good reason.
All the time trials for kidney transplants. Not only is it extremely difficult to remove the old kidneys from their original locations, it can be a real pain to place the replacements in a way that triggers the win condition. You are going to tear your hair in frustration over these ones.
"I Can See For Miles... Per Hour" is especially bad on the PC. On the Playstation, you get 2:20 to finish. You only get 1:40 on the PC. Add on the fact that you have to do this in an ambulance and you have one of the most frustrating achievements in the game.
"Best Surgeon In The World". Get perfect scores on all operations, which requires losing as little blood as possible and completing the operations in reasonably short time. Easy enough with heart surgery, but increasingly difficult with subsequent surgeries. And good luck with ambulance/corridor/space mode.
"A Small Loan From My Father". You have to rack up a bill of $1 million on the Trump surgery and finish it. To explain how hard this is, you cam take the hatchet to Trump's face and only barely pass the threshold while killing him. Managing that bill while also saving him is next to impossible. So impossible, in fact, that the devs actually acknowledged as much and promised to rework it so the achievement wouldn't be luck-based, which resulted in it being only slightly less impossible to pull off.
Ambulance Brain Transplant. Trying to clear out the skull and separate the brain stem while avoiding damage to the most sensitive organ in the game is incredibly frustrating with the constant motion, especially if you're going for A++. Doubly so because, as noted above, the patient can die through no fault of your own. The space version is actually easier because the brain floats up and makes cutting the brain stem a breeze.
A better example would be all of the kidney transplants. Not only is it difficult to remove all of the organs that are in your way without blood loss (especially since one of the spots where you can cut the large intestine is buried underneath the small intestine), but also removing the old kidneys is a pain (especially the left one; your best bet is to use a spoon to move it around), and placing the new ones in a way that triggers the win condition is easily the worst of all the problems. Oh, and you think that's bad enough in the normal mode? Try doing that in the ambulance and space ones...