The hurry is the least of the problems with the writing. Off the top of my head:
* Why go back to such a last-minute point? Why not go back to when, for example, Soran was on the Enterprise and you had transporters, security guards, and forcefields?
That's pretty simple and strikes at the root of the issue. If Picard apprehended Soran, all would be lost, because (as far as Picard knows) Soran's doomsday weapon would be in the hands of the Klingons whose whereabouts were unknown back then. By going back to a point where the twisted sisters were under the guns of the Federation Flagship, Picard could exert a measure of control.
The farther back Picard goes, the less control he has. Between then and now, anything can happen. If he tries to alter B in the distant past, he'll lose forever the ability to alter A here and now. Stop the Borg, how? They were stopped by a fluke as matters unfolded; Picard couldn't trust himself to do any better a putative second time around - and he would certainly lose track of Soran's starkiller if trampling on butterflies that far back.
* Assuming you want to bypass the easy sensible route as described above, why is Kirk picked? I know, if you can go to when ever, why not pick up somebody that's really an ass-kicker, or how about taking weapons or a ship with you?
Whom would Picard know? The movie established every reason for him to suspect Kirk would be aboard. There would be none for him to think Clark Kent would be available.
* And why only one person? How about ganging up on Soran?
Again, with whom? Picard can dream up a whole army, but dreaming up will lead to his destruction - clinging on to reality is his only hope of ever achieving anything real. Hard to tell if he achieved any as matters now stand, but it's at least a theoretical possibility that he really stopped a real planet from blowing up for real.
* How do you even know you left the Nexus for certain?
This isn't a plot problem. It's a plot-enhancing feature.

* How did you leave the Nexus? If you can't fly a ship into it and the only way found to possibly get in is to let it sweap you away on a planet's surface (which, by the way, how in the world do you find out that is possible?), how in hte world do you exit it so easily?
Obviously the thing grants you all your wishes. But only once you are aboard! You'd get VIP treatment, complementary drinks, and precision paradrop at your request once you managed to board Air Force One and flash your psychic-paper ID, but jumping onto a speeding jet flying over you at 20,000 feet is gonna be tricky.
* If you can pick the solar system, galaxy, planet, and spot on the planet you can get back to along with a general time frame, why can't you put yourself someplace useful, like at the controls of the rocket?
For a moment, I got this vision of Picard bronco riding the toy rocket...
But as we see, Picard can't operate the rocket. And stopping Soran will stop the rocket. Stopping the rocket won't stop Soran.
* Man, of all the potential people inside the Nexus, what dumb luck you happen to not only run into another human, but a Starfleet officer and a previous Enterprise Captain! Lucky break is lucky break!
The Nexus does requests. What else would Picard have been able to ask for? He knew Guinan, and he knew about Kirk. He didn't want to meet Soran's echo. And that's pretty much it.
* If in the Nexus time has no meaning, then how does the Nexus know what time you are thinking of to go back to?
It has a well-designed user interface. Why would it have a poorly designed one?
* How do you communicate with the Nexus? Is it sentient? Sentient enough to keep you alive, communicate with you, send you back in time, but not enough to avoid ships and planets.
Why should it avoid planets? Going to planets is a good thing - that's how passengers can get aboard. And ships stumble onto its path at their own peril - a cruise liner can't dodge every stupid peanut shell trying to sail across her path. The purple color should be a warning horn of sufficient loudness already; if you see purple mist in Trek, it's usually about horrible death or worse.
* If again avoiding the easy sensible route from the first example, doesn't Kirk know anybody esle there that he can tell something along the lines of, "Hey, could you wait five or ten minutes, then come after me incase I get shot in the back like a little bitch?"
Why should Kirk know anybody in there? He just arrived. At best, he might ultimately meet some of the El-Aurians who got sucked in. But he hasn't even had time to wrap his brain around the idea that he could ask that of the Nexus.
* How does it know which reality to send you to? If you have to tell it, how do you know which reality you were from?
That goes for every time travel adventure in Trek, too. It just happens that you always find the correct branch of the timeline. Or then Ziggy does it for you.
We've seen one episodes where the boundaries of time and space break own and multiple Enterprises appeared, so we know there are tons of alternate realities, so if the Nexus is a convergence of time and space, they're all mixed up and jumbled in there. So, how do we even know Kirk is dead? Is that the Kirk from the timeline of the show or a Kirk from an alternate reality? Then Kirk could still be alive in the Nexus. There could be hundred of Kirks in there, overwhelming tiem and space with the magnitude of awsome they have.
Which is all to the merit of the Nexus concept, not to its detriment.
Timo Saloniemi