I have only read one other Wimsey novel and I do think that
Gaudy Night is a considerably better book—though it is perhaps really a Harriet Vane novel.
For an opening attempt at the genre
Whose Body is a reasonable effort. It has some humorous moments—particularly the inquest. The relationship between Bunter and Wimsey is seen to have a certain depth deriving from incidents in the Great War. I think the meeting between Wimsey and Sir Julian Freke near the end was competently done. At that stage in the book the drama of the mystery was beginning to wear a bit thin and some type of dramatic confrontation between the two was necessary.
The murder itself was certainly ridiculously complex. I suppose one is meant to suspend logic at such times. After all, consider the famous crop-dusting scene in
North by Northwest. Who would really try to kill someone with a crop-duster in a cornfield?
Likewise, if Freke is really the brilliant murderer he is, surely he could have used a method that was simpler but equally deadly—such as the poison he attempted to inject into Lord Peter. But I suppose that much of the pleasure of such works lies in the fact that the means of choice
are outrageous.
Anyhow, while I suspect from the comments of,others, that Sayers improved as the series developed, I was mildly entertained by the book despite the limitations which others have rightly noted.