Sci: While I hesitate to bring real-world politics into the discussion, one of the results of the Clinton impeachment thing in 1998 is that more brilliant legal minds than anyone who's ever likely to come to this forum looked over the law and precedent re impeachment with fine-toothed combs that practically worked on the quantum level.
(I'm only being a mite hyperbolic.)
The end result is: If the UFP's relevant constitutional provisions are anything like the US's, "high crimes and misdemeanors" means whatever the legislature wants it to mean, no more and no less.
(You might agree with Clinton's impeachment, you might not, but I've not in 12 years heard anyone say that Congress didn't have the power to impeach. Whether they should have or not, sure. But whether they could or not?)
See, the problem with that argument is that Clinton was accused of a crime: Perjury. The relevant question with Clinton's impeachment was whether or not he had committed perjury, and whether or not perjury constituted a high crime or misdemeanor.
The issue with Jaresh-Inyo is simply this: Is appeasement -- a foreign policy trait that is difficult to define in the best of times -- considered a high crime or misdemeanor by statute? As I noted, it would be exceedingly difficult to make a law against that, because whether or not a given policy is actually appeasement can be very subjective. So the relevant questions here are, Is it a violation of Federation law for the President to engage in appeasement?, and, How can you prove that a Federation President has engaged in appeasement?
But either way, the Council can't just impeach someone for something that isn't a crime. A law has to be passed against something first. So the idea that they can just call anything they want a "high crime or misdemeanor" is just wrong.
Judicial review is also inapplicable if the UFP's justice system uses anything like the Common Law system used by (most of) the US, England, etc. I suspect they do.
The episode "Dr. Bashir, I Presume?" rather strongly established that the Federation uses judicial review. In that episode, Dr. Bashir's father, upon his son's secretly having been genetically enhanced as a child is exposed, vows to fight the law banning genetic enhancements and get it overturned, even if he has to fight all the way to the Federation Supreme Court.