Broken Base: The game itself to the fanbase, with half of it hating it for the changes and the other love praising it for them. Its story is also divisive, with changes to Nod and Kane's characterization and Kane's plan itself being divisive between people that consider whether or it makes sense.
Idiot Plot: The plot of the entire game hinges on a complacent and downscaled GDI putting the Achilles' Heel of its entire Kill Sat network on Earth (where it isn't protected by said network), in a small, poorly defended base. The GDI campaign reveals this was a decision born of cost according to GDI bookkeepers... some of which were later found out be NOD Deep Cover Agents
Moral Event Horizon: Kane's deliberating arranging for the destruction of Eastern Europe as part of his plan. Even followers in game question it.
Director Boyle's decision to fire the Ion Cannon over General Granger's objection is this as well. He isn't questioning the legitimacy of Granger's concerns; he just doesn't care.
Special Effects Failure: Kane's mask in the first portion of Kane's Wrath is noticeably lopsided. This is most noticable if you look at the top of the mask and the part next to his left cheek; the angle of the slant on top would have been corrected if the left side of the mask actually touched his cheek instead of just hanging there. Becomes Fridge Brilliance when it is revealed that Kane is perfectly normal under the mask, the mask being a mere decoration.
Tear Jerker: In the cutscene that plays when starting Act IV of the Nod Campaign, it's hard not to feel some sympathy for the Nod-affiliated field journalist in the news video. Watching his people faced with impossible odds, believing that all is lost, and spending his dying moments reciting a Nod prayer before GDI fires the ion cannon...
GDI's mission to destroy to port of Alexandria (Hard mode) is one mission where nerfing in multi-player has a poor result on the single-player missions. Your adviser who briefs you encourages you to build Mammoth tanks and roll over the NOD port authority base, but the Mammoth is a poor choice for direct assault because of the infiniteresources fueling the enemy's constant assault, and the severe lack of money for you to harvest. Also, the tanks are too under-powered to handle the job, and the rail-gun upgrade to increase their firepower is a ridiculous $5,000 (that's the price of a superweapon). Because of this broken mission, you're better off holding the line and using Orca aircraft or a Zone Trooper force to surgically strike the targets, quickly ending the mission through brains.
Nod's final mission, named Kane's Tower, requires the player to defend three Scrin Phase Generators from GDI, which sounds simple enough, until you realize that you're severely handicapped by the following factors:
GDI is shelling the structures you're supposed to protect from the second the mission starts with unique artillery that out-ranges normal artillery by a factor of 5- captureable, sure, but only if you manage to get to it while simultaneously dealing with all the other difficulties at the same time with your very limited early game resources.
You start out with one medium sized base at tier 2, GDI starts with two tier 3 bases, one of which is larger then yours, and the other much larger.
The Scrin are hostile to you, making protecting them difficult, but they're also nowhere near powerful enough to stop GDI.
GDI will happily build not one, but two Ion Cannons before you can even begin construction of your own Nuke.
GDI starts with a fully functional small airbase, which will bomb the Scrin to the ground if not disposed of
Your two starting Tiberium fields are both in harms way, one from the Scrin, the other being the main avenue on GDI's attacks on your own base.
And to top this off, GDI's units instantly reach elite status, and would gain heroic status in as few as a single kill.
Given all the above factors, winning the mission often depends on luck more so then anything, as the GDI attacks on the Scrin vary in size, from manageable, to an armored column consisting of a dozen Mammoth Tanks supported by twice as many lighter vehicles and about as many infantry squads, as well as every single reinforcement support power in the GDI arsenal. Losing (which will happen very often) will earn you a chewing out by Kane himself, despite the fact that his request to protect the Scrin structures from such an onslaught is completely unreasonable.
Operation Stilleto (which comes shortly before) is also frustrating for very similar reasons; you are tasked to take over 2 construction yards each from the warring Scrin and GDI. Taking one is easy enough, but that often results in the weakened side losing their second construction yard soon after depending on how the AI's fight. And you won't have the firepower needed to stop that before you captured the first one.
The final GDI mission can be pretty though as well, if you don't use the Liquid Tiberium Bomb (which will essentially wipe out Nod or most of the Scrin). You have to quickly build up forces to eliminate (or capture) the Scrin Superweapon right away, then to deal with their mothership or divert it to Nod, all the while both sides will attack you early and often, including building more Superweapons and advance bases.
"A Grand Gesture" from Kane's Wrath also qualifies. You WILL be attacked within two minutes by swarms of GDI Vehicles and infantry. And they don't let up. Ever. It's also the first mission where you play as the Black Hand subfaction. Finally, good luck getting to those downed Purifiers. They make the mission a lot easier, but having one survive long enough to make the trip back to base for repairs is harder than it sounds.
Moreover, some players were really salty that Tiberium lost its pod.
They Wasted a Perfectly Good Plot: Kane's Wrath only has a campaign for Nod. This is especially baffling when Kane admits that inbetween the final Time Skip GDI wiped Nod off the map, which sounds like plenty of opportunity to give GDI a campaign. Particularly considering the expansion introduced two subfactions to GDI that were ripe for campaign scenarios.
Though it should be noted that Kane's Wrath was titled "EP 1". Presumably, more expansion packs focused on the other factions were planned, but never came into fruition.