- Trump's lawyers argued in this case that an ex-president can only be charged with a crime if he was impeached and convicted for that same act. But all of the justices rejected this view today. The newly granted immunity is orthogonal to whether or not the president is impeached.
- Though, the president does have to leave office somehow before he can be prosecuted. He can't be prosecuted while still sitting. This wasn't technically decided in this case, but the parties mostly agreed as much beforehand, and the majority opinion has a footnote approvingly citing an Office of Legal Counsel memo to that effect.
- Separately, Trump's lawyers argued that the special counsel that prosecuted him was not properly appointed by an act of Congress. But the Supreme Court did not grant certiorari on that issue and the majority opinion today did not address it. Justice Thomas's solo concurring opinion, however, did address it and agreed with Trump (but a concurring opinion has no legal effect). In any case, this is a different question from whether prosecutions of ex-presidents must go through a special counsel. As far as I know, there is no formal rule that would require it, but it's highly desirable as a way to avoid political bias. That question didn't come up in this case, though.
Trump's attorneys did not say "the special counsel that prosecuted him was not properly appointed by an act of Congress", Justice Thomas brought this up in oral arguments. Trump's attorneys admitted in oral arguments that they had not brought this up during the appeal, so as an argument it was not saved.
Further more, historically there is no basis for the argument. Special prosecutors, which are different from the "independent counsel" that came about after Nixon; the laws around "independent counsel" expired a while ago.
"Special counsel", and all of the other similarly named, have been around since Marbury. By happenstance, some have been X-members of Congress, Cabinet members, etc... but far from all.
There is a reason why none of the other Justices brought this up, it is absurdist.
- Trump's lawyers argued in this case that an ex-president can only be charged with a crime if he was impeached and convicted for that same act. But all of the justices rejected this view today. The newly granted immunity is orthogonal to whether or not the president is impeached.
- Though, the president does have to leave office somehow before he can be prosecuted. He can't be prosecuted while still sitting. This wasn't technically decided in this case, but the parties mostly agreed as much beforehand, and the majority opinion has a footnote approvingly citing an Office of Legal Counsel memo to that effect.
- Separately, Trump's lawyers argued that the special counsel that prosecuted him was not properly appointed by an act of Congress. But the Supreme Court did not grant certiorari on that issue and the majority opinion today did not address it. Justice Thomas's solo concurring opinion, however, did address it and agreed with Trump (but a concurring opinion has no legal effect). In any case, this is a different question from whether prosecutions of ex-presidents must go through a special counsel. As far as I know, there is no formal rule that would require it, but it's highly desirable as a way to avoid political bias. That question didn't come up in this case, though.