Howard Payne deliberately rigged the bus with an elaborate hydraulic suspension system so that it could allow the bus to clear that jump if necessary.
I might be going out on a limb here, but considering how Howard had gone and rigged not just one, but another smaller bomb for the escapee, there wouldn't be any better explanation than for Howard to have installed such a system as a means to further prolong the situation and toy with the hostages more, if it meant getting the ransom or otherwise.
- It should also be noted that upon the bus jumping, it is launched upwards without the use of a ramp as if it is being propelled by hydraulics from underneath.
It was certainly better quality than Speed 2.
Howard Payne's career-ending injury wasn't just his hand
Considering the man's insanity, it's possible, even likely, that the explosion that injured his hand and ended his career had also injured his brain. Besides his injured hand, there's also a scar on the right side of his neck. He could've sustained blood loss or a concussion from any shrapnel and the blast wave. Brain injuries can change personalities. Pre-injury, Howard Payne probably would never have even thought about such a plan. Even if he had faced early retirement with just an injured hand, the man could've easily made money by other legal means as a consultant or started his own business (his workmanship seems second-to-none).
Payne used the security guard's body to fake his own death.
At the award ceremony for Jack and Harry, the commissioner (or whoever) even mentions "only the bomber" died, even though Payne killed the guard who caught him monkeying with the elevator controls. And to think Payne died in the explosion, the police would've needed to find a body. So after killing the guard, Payne rigged him with explosives and stuck him in the parking garage, then set the bombs off after escaping. This is, after all, explicitly what he plans to do with Annie later. He tells her "Mess like that, they don't count body parts, gives me more time," implying that in such cases the authorities wouldn't bother ID-ing the body and just assume it was the perpetrator's. By the time they do figure out it's not him, he's long gone with a solid lead.
Payne faking his death using a bomb vest and another victim was his exit strategy
Up until the moment that Howard blew up the city bus, the police thought he died in the building explosion. No one even missed the security guard.
His police uniform disguise and second bomb vest wasn't a backup plan or a revenge plot, but his exit strategy. His plan would've gone like this:
1. He waits for the money to be dropped off.
2. He dresses up as a police officer, accosts some bystander or worker, dresses him or her in the bomb vest and has that person retrieve the money from the drop.
3. If the police respond, he has a hostage that forces them to back off. If not, he'll just call attention to himself by shooting into the subway station ceiling so there would be witnesses.
4. He and the hostage board the subway train, but he clears it of other passengers except for the motorman. It's likely that specific route has his exit.
5. Once moving, he kills the motorman, gets off the train somehow, gets to a safe distance and detonates the bomb. The resulting chaos gives him the time he needs to escape. He then just gets to the street level, gets into a non-descript vehicle he has stashed somewhere and hits the road.
He choose Annie because he recognized her from the bus and knew that Jack would be less inclined to risk her life as well as revenge for fouling things up yet again. Even if there weren't snipers watching the drop point, he could've detonated the bomb on the bus regardless to serve as another distraction. Or just for the fun of it.
Would the police fall for this scheme a second time? Knowing he had already pulled the same stunt once, they'll likely operate on the assumption that he's still alive and put out alerts with his name and face at every airport and border crossing. To beat that, he could cross the border in some remote spot or just go to a marina, board a chartered or purchased boat, and sail (or motor) away. From there, he just has to deposit the cash at a bank that doesn't ask too many questions and he's all set.
Even if the authorities found out he was still alive, he may have planned for that during the elevator job. Spending two years just to rig one elevator car would've meant not just building the equipment and scouting the location, but also research on the best route out of the the country, finding a safe location to deposit the "retirement" money, and having somewhere to go that's safe for him to live out his days. Jack foiling his elevator job meant that everything else he had lined up for his escape got screwed up too. Bribes for getting through customs and a down-payment on a private island are examples. Hence the higher ransom for the bus.
Annie knowingly transferred the dye pack into Howard's bag
Given everything she had gone through that morning, she knows how crazy Howard is and that it was highly likely he was going to kill her. So, when he had her transfer the money into his bag (and probably warned her about the tracker and the dye pack), she filled the bag and
knowingly transferred the dye pack in anyway to
screw him out of his money. Howard was holding Jack at gunpoint, so he kept his eyes on him instead of Annie, which would give her an opportunity to spot the dye pack and put it in the bag. It exploded on the train because he started sifting through the bag looking to bribe Jack; which Annie didn't expect him to do until after he killed her or she got rescued. When the pack goes off in his face, you can see a hint of a grin on Annie's face. Instead of blaming her, he blames Jack since he is still after him and keeps getting in his way.
