I saw that cover too and got a good chuckle. I was starting to wonder if there was going to be a cover that showed the key evidence visible in the bathtub.
A few people already commented on the voting thread that this is not necessarily a good starting place to see the best of Lord Peter. It seemed to be a book of great potential, but never quite make it. Too much happened "off stage", only to be chatted about later by Lord Peter and his friend Mr Parker. And most disappointing of all was the disaster of a wrap-up, with the great long confession over-explaining every detail. A real "first book" mistake of not trusting your readers to have kept up.
I rather liked the preface added to the newer editions. I felt this tongue-in-cheek biography gave a neat synopsis of the character while - more importantly - giving you a good idea what to expect. I found that it let me jump straight into the story and accept Lord Peter for what he was, when otherwise I think I would have been floundering for a while trying to work him out.
I am curious as to whether the characters would have felt like stereotypes back when they were written, or is that only what they've become since that time? But rather likeable/enjoyable stereotypes for the most part, which is why I think the book had so much potential. Certainly there was enough fun in the early part of the book that I'd give a few more books a try to see if Sayers gets better.