There are a handful of river exceptions and these make sense to me, e.g. Columbia is a massive river that divides WA and OR, same with the Snake River and OR/ID and the Colorado between CA/AZ.
I assume Idaho-Montana is along some mountain ranges, but is there a reason it got divided up this way, while other mountainous states like Wyoming and Colorado are just plain rectangles?
Slightly related, was there a reason they left Idaho with the little panhandle connecting to Canada? Was there some historical reason for Idaho wanting to claim that, or it's just the way the borders fell between Montana and Washington?
I refer you to Mark Stein's book, How the States Got Their Shapes. The original Idaho Territory, created in 1863, had its capitals in the gold rush towns of first Lewiston in the north and then Boise in the south of modern Idaho. The territory itself spanned all of modern Idaho and Montana and almost all of Wyoming. That territory lay on both sides of the near impassable mountain ranges that make up the Rockies. The Continental Divide runs right through it. The area of modern Montana was essentially totally cut off from the government in Idaho for months at a time.
Enter Sidney Edgerton. He was an ardent abolitionist and friend of President Lincoln's. He was appointed to the post of Chief Justice for the newly created territory. The governor, however, posted him across the mountains in Bannack, now Montana, far from the territorial seat. He didn't take that lying down. Gold was discovered there, and he quickly set out for Washington bearing about $2,500 (at the time) worth of it. He lobbied Congress and the President to split the territory. It was done, and Edgerton was made governor of the new territory of Montana in 1864.
The divide in the territory was set along the mountain peaks, specifically along the Bitterroot Range of the Rockies. There's a myth that it was originally intended to be the Continental Divide, but that's not the case. Edgerton was determined advantage Montana in the division, and Congress more or less went along with him.