Alright, having looked at it more, I see some problems...
1) According to the Convetion of Genocide,
5. (1) Nations must facilitate the extradition of those suspected of the crimes specified in section 4 to the appropriate authority should they have escaped outside of the appropriate authority's control, subject to national and international law.
(2) The crimes specified in section 4 may not be considered political crimes for the purposes of preventing extradition proceedings.
I do not know what "appropriate authority" is, but I strongly suspect that it refers to the nation in question where the genocide has taken place. So, if a genocider committed genocide in a WA nation and fled to another WA nation, that second WA nation must extradite the genocider over to the first WA Nation.
So, since the Convetion already handles how genocide gets prosecuted (hand it over to the country where he commited the crime and let him meet justice there), a lot of the court work of the Court goes away. To be fair, you are including other stuff too...but...
2) The Court has the power to administer any sort of punishment it wants. For my proposal, all I wanted was just a fine on the war criminal in question. You're allowing the Court to propose whatever punishment they want. What if the Court decides the death penalty? Or some other cruel punishment? TPP only allowed for a life imprisonment, at its most extreme.
3) In Noordeinde's proposal, the Court's definition of crimes appears to be a laundary list of deeds that the proposer in question does not like. The actual definition is that war crimes and Crimes against Humanity are "widespread or systemic atrocities" committed by persons against "civilian populations", and the laundary list is just a list, it may be extended whenever the Court desires, as long as the Court determines it to be widespread or systemic. That just begging for the Court to abuse its powers.
And the crimes you mention such as Rape would mean that the Court has the power to basically drag a serial rapist into the international court system and try him like a war criminal!
And deportation? If somebody is illegally within my country, I'm going to instruct my police force to deport that person. I'm NOT going to get myself dragged into the international court system and get punished as a war criminal.
Further, you criminalize "any other inhumane acts of a similar character intentionally causing great suffering, or serious injury to body or to mental or physical health". That's swell. So, if a cop uses a loudspeaker to scream at protesters, "DO NOT RIOT!" I have no choice but to arrest that cop and send him off to the UN Court system? I mean, he is intentionally causing great suffering and possibly serious injury to the hearing of the protesters in question. In any event, if the Court wants to summon my cop to a trial, and if I'm in the WA, I have no choice, I'll give in.
4) Who is this President mentioned in Article 4, Clause 5? Is it the head of this Court?
I'm interested in creating my own resolution about a world court, considering that I don't really like this one, but I do understand where a world court might be useful. Like in settling border disputes.