The only specific reference I can find to the two distinct covers for the same Plume first printing of The Waste Lands is in this book listing by Locus Magazine:
The Dark Tower III: The Waste Lands (Penguin/Plume 0-452-26740-4, Jan ’92 [Nov ’91], $15.00, 422pp, tp, cover by Don Brautigam & Phil Heffernan) [Roland (Gunslinger)] Reprint (Donald M. Grant 1991) dark fantasy novel, third book in the Dark Tower series, with full-color illustrations by Ned Dameron. There are two different versions of this edition, one with a cover by Brautigam, the other with a cover by Heffernan. Other than the cover illustration, the two are identical.
It doesn't give an explanation, but does seem to confirm that it is not simply a misprint. Further evidence for it not being a misprint is that the artists are listed correctly on the back cover of each version: Brautigam is listed as the front cover artist on the rose-cover edition and as the back cover artist on the train-cover edition.
We should also note that it is not unusual for King novels to have dual covers for the same edition and printing. For example:
Insomnia: Published in 1994 by Viking. Trim size is 6.25 x 9.5 x 2.1". Dust jacket price is $27.95 and code on dust jacket is "1094". The book is quarter bound in light gray cloth with gray boards. Paste-downs and front and rear end papers in gray. "First published in 1994 by Viking Penguin" and the code "1 3 5 7 9 10 8 6 4 2" on copyright page. Two simultaneous dust jacket states with red and white reversed were issued. Both have same value.
While King hasn't explained the dual covers for Insomnia either, there is an interesting passage in that novel:
It was as if his eyelids had turned to glass. The only difference was that all the usual colors had reversed themselves, creating a world that looked like the negative of a color photograph.
One can speculate that the dual covers find their meaning in this passage.
So, while I cannot find a direct explanation for the dual covers for The Waste Land, it seems to be something that King has employed more than once for his novels (and it may reflect some specific idea within The Waste Lands).