- 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.