I'm just gunna say one thing: if you've got a honkin big remote controlled gun, why would you sit in the park next to it? Why not phone in the kill from Venezuela or something? Complete Idiot Plot.
His remote had probably a limited range because a stronger signal would be easier to home in on. If the secret service is looking for unusual signals that can be used to trigger a bomb/control a gun the weaker the signal is the better for him. He also has video on his remote which needs a higher bandwich, so the internet of 1997 is not going to able to give enough of it. And if he got himself a dedicated data line/satelite connection (like tv crews do for their live reports) these are easely traceable (and for a high profile event booked for month in advance). His plan wasn't bad - at least not that part of it.
Also, the gun is very big, and he is the only person putting everything together. He would need a car (which he himself would have to drive) in order to both transport and conceal it. If he had tried to remote-control it from Caracas, he would have had to had put everything in place several days beforehand, running a significantly greater risk of the whole thing failing by way of mundane occurances, whether the First Lady's speaking engagement getting changed (perhaps it rains that day) or some curious bystander or cop looking in and wonder why the hell there's a huge-ass gat propped up inside a parked minivan.
Controlling it from Caracas is impractical, but actually staying around on the scene was also impractical. The best place to control that gun from would have been about six blocks further over; as is, the Jackal stayed within the immediate search perimeter of the first people who'd be alerted by either the gun's discovery or its use.
Here's another one: $70 million USD to kill...ANYBODY. Who would pay $70 million to have a single person killed? How would they pay you? WHY would they pay? If you got away w/ it,you'd be hunted down anywhere in the world and you would certainly be "convinced" to give up the people that are paid you. VERY stupid movie.
Eh, it is a stupid movie, but you're ignoring the motivation. The $100k question is, why would a Azerbaijani mobster put that kind of resources into avenging his dead brother? That "single person" ended up being the First Lady and Jackal openly said it would have to be his last job. And the $70 million was the figure Jackal himself threw out, him being an implied world-class assassin also implied he knew what kind of money it would take to keep himself safe in retirement. That part was was actually very faithful to the book (sans the gratuitous fee, even accounting for inflation).
How was Declan able to piece together from the line "he can't protect his women" that the real target was the First Lady and not the head of the FBI? Was there something else I missed?
"Remember: public, but brutal." It's likely the original dossier that had Donald Brown was a red herring so that the FBI would focus resources on keeping him safe and out of the public eye, while leaving the First Lady out in the open to do a speech at the opening of a children's section of a hospital. My impression is that Declan knows the Jackal's MO, and going after a well-protected but not really that visible figure in the government didn't fit. I suppose then it raises the question of why the Jackal gave that information in the first place.
The Jackal was becoming more and more sloppy and unhinged as the movie wore on - perhaps he simply fell into Hollywood bad guy mode.
Forgive me if this seems obvious but... what the hell is that magic spray he uses to kill the hijacker? and why isn't he carrying this rather potent chemical weapon around with him at all times? After all it appears to require only the slightest contact and I'm sure a man as cunning as him could have found some way to introduce this to Declan during the subway chase.
He probably considers it too dangerous, even for him. If he's chased and falls, or shot at, or punched the wrong way, the canister could crack, to the immediate lethal detriment of whoever's holding it.