The following function, which I mailed out to this last last February, was intended to demonstrate how CALL-WITH-CURRENT-CONTINUATION could be used to expose the SET! hidden in the definition of LETREC:
Notice that the variable STATE does not occur anywhere in the right hand side of its own definition in the LETREC. Thus you might think that you could optimize this into an instance of LET. But that optimization would be incorrect (assuming that the expansion of LETREC given in R^3RS really -is- its definition), because then this code will stop producing side-effectable cells.
(TEST) should return #T. If you replace the LETREC with LET (you might be tempted because X does not appear anywhere in the right hand side of the definition!), then (TEST) will return #F.
I wonder if any real compilers make this mistaken optimization?