Picked up a copy of the movie yesterday morning, together with 'Southern Comfort' (excellent) and 'The Cincinnati Kid' (to be saved until later).  Three for a quid, so not bad value.
It's years since I watched it on TV, so I'd forgotten some of the details.  What interested me more than the plot, though, was how costume had decided to dress Walken's character.  First time you see him, reading to his students, he really does look like a bad caricature of a geography teacher, hair and clothes nerdy beyond belief and making the way UK Ivy heads wear the tan cord sack look cooler than ever.  Then, on the rollercoaster, they put him in quite a nice duffel coat.  Later, he's in a dark coat - not, I don't think, a pea coat - with the collar up, because there's always snow on the ground.  He looks pretty cool in some of those later scenes, because Walken is often (not always) a pretty cool kind of personality.  The button-downs, though, seemed few and far between.  Martin Sheen, I guess, was supposed to look like a God-Bothering Tea Party-type dork.