I love the "Play Against Bobby Fischer" lessons by Igor Khmelnitsky, but surely there is an error in lesson five. Black misses mate by moving the queen instead of the rook. Maybe Fischer goofed, but it seems unlikely, and even if he did, it kind of spoils it as a lesson.Or am I wrong?

Checkmate is always a good move.

In lesson 5 there is no checkmate with the rook. After 1... Rh1 there is still Bf1.

However, after doing some analysis I must say the lesson is total crap. The variation given by Khmelnitsky is just bad play by black as it lets white's king run away.

As white is more or less in Zugzwang black seems to win after simply going exd5 and Computer already gives -2

 Yes, the runaway king is what I recall resulting from the (alleged) solution.

I can't get into the lesson right now to check the board to see your Bf1 move preventing  what I thought was mate with the rook. But I will check it.