The entire movie was stolen from some earlier Trek and crammed together in a very dumb way. Not to mention that the film is so static and lifeless. It's like the movie is trying to force me to fall asleep. The direction is crap, the acting is crap, the story is crap, and the action is uninspired.
The whole thing is so implausable. The timeline goes something like this, if we assume Shinzon is 25:
-The Romulans clone Picard, captain of the USS Stargazer.
-When Shinzon is maybe 10 they decide to make him a Reman slave.
-The Remans for some reason give a shit about an alien kid and help him.
-Shinzon spends 10 years underground.
-The Remans make Shinzon their leader...? For some reason?
-Despite the fact that Remans are 'canon fodder' Shinzon is given command of romulan forces during the dominion war. (he's what, 17 years old at this point?)
-Shinzon builds an uber-ship with technology far more advanced than the federation or romulan ships. Without the romulans finding out.
-Shinzon finds a Soong android somehow.
-He somehow reprograms it.
-He leaves it on a planet near the neutral zone, scattered in pieces.
-He kills the romulan senate with the help of the military.
-By random chance the Enterprise is sent to romulus rather than any other ship.
-Shinzon, after waiting his whole life for his moment of glory, sits around jerking off for the better part of a day.
-Shinzon uses the B-4 android to steal starfleet's info. Which he doesn't need anyway.
-Captures Picard FINALLY but then doesn't steal his blood, or destroy the Enterprise, or warp to Earth. Everyone just sits on their hands until Data saves Picard. THAT WENT WELL.
-Romulans turn on Shinzon because they...want to save Earth...despite having given Shinzon power so he COULD destroy the entire federation. Yeah, whatever.
-blah blah blah.
-Shinzon is killed by a...pointy wall decoration.
It's all nonsense. I've read fanfics that made more sense.
You pretty well summed it up in nice concise bullet points. The key elements for me are:
* Shinzon's character - we have no back story that makes sense for the person we see. Picard is much smarter than average, but he's no genius. Thus, Shinzon can't be either. Then what does he have to offer? The Romulans would have killed him, not put him into slave labor. As a child? What good? Kill him. But no... he grows up in slave mining. No education. But the Shinzon we see seems quite educated. It makes no sense. Growing up in that situation... even if the Remans befriended him, he'd be a "human trophy" for them. Not a leader. It makes no sense.
* Shinzon's technology - no plausible way for him to have developed such a superior ship AND develop the biogenic weapon. Remember in TNG, the detection of the metagenic production? Certainly the Romulans would have detected any biogenic development. The Remans are treated as 2nd class citizens... no way that anyone could get the resources it would take to build something like the Scimitar.
* Shinzon's hatred - for his back story, there would be no more compelling foe for him to want to eradicate than the Romulan empire. And I'd expect he'd crave to seek out Picard as a father, not as a nemesis.
* Thalaron radiation - 'Radiation' identifies a certain kind of property. This 'thalaron' biogenic weapon does not behave as such. After the incident in the Romulan senate, no one would be able to go near it for years. The Scimitar's destruction would have given off thalaron radiation and killed everyone in the area. There's no radiation, so don't call it that.
Yeah... these glaring and ridiculous issues. I'm so very surprised that Berman had the power to get this out... wouldn't SOMEONE with even the slightest pull at Paramount say "Hey, this is CRAP--we can't make this as-is; it MUST be rewritten," especially given the enormous budget?