So let me get this straight about the ending: Mal came to the hotel room, made a mess, toppled the furniture, then leapt across the space to the opposite window… Wait, what? I guess she could have made a mess and then snuck to the building across to startle Cobb, but why make a mess? Just leave the window open. Not like he’ll ignore an open window.
And anyway, what’s with her “trap”? It doesn’t make sense. All Cobb needs to do is wave and yell the moment she hits the ground. Somebody sees him at the window, instant bulletproof alibi! The street below them has 4 or 6 lanes at least. How’d he push her out of a building that far? Why is there no sign of struggle? Any competent lawyer will get Cobb off the hook in a flash. And surely it would look fishy when a psychiatrist examines the children and they don’t seem abused or in danger from Cobb?
Now, I’ve never heard of such a thing as being “declared sane”. Sure, there’s documents you get for driving licenses or diving cards and what not, and they include mental health. But all that means is the doc checks if you ever got sent to the funhouse, and your behavior with him obviously shows you are not completely batshit. So they sign you off. That’s it. Maybe you lied, maybe they didn’t ask the right questions, maybe you are actually a psychopath inside, obsessed with acting out Carmageddon in real life. He wouldn’t know! These things are a 5 minute visit to the doctor, and all they show is whether you have overt, very obvious issues. The legal system is probably aware of this, so saying “hey, she was sane enough to drive!” is a bullshit defense.
As for a more thorough examination, you simply can’t take someone and say they are “completely sane”. Just checking for one disease takes many sessions over weeks, and the DSM has hundreds. The psychiatrist’s job is hard enough with willing clients who try to helpfully describe their issues, it would be trivial for a crazy person to fake sanity (Obviously, there are extreme cases. If a guy walks in wearing a tinfoil hat and starts checking the room for bugs, yes he is obviously out there. But just because he doesn’t, can you say beyond reasonable doubt that he isn’t paranoid?). This is like TSA asking travellers if they are a terrorist. I mean… Geez.
So how Mal obtained such documents, such that they are hard proof of her sanity, is beyond me. But that’s not the only problem. See, even in a fantasy universe where this is possible, wouldn’t someone obtaining unusual documents proving their sanity, just before committing a rather insane act, look a wee bit suspicious?
In all honesty, Cobb should’ve just gone to court. Doubtless his occupation could pay for a decent lawyer, I’d be surprised if he didn’t have a team of them already.
And finally, why bother with Saito just to see his kids? So he can’t enter the US. Well, move to Switzerland and take the kids there! Genius idea, I know. Is it the grandmother? Get one of his teammate to kidnap them. They know the reason is solid, and even if not they are all immoral knaves anyhow. The most the relatives can do is probably file a missing person report. Cobb is a man adept at disappearing from powerful multi-national corps. Sure, he botches this in the movie, but I can’t imagine him surviving in his job without being good at it, and he implies he is.