I definitely had a different cover to my copy that you did - it was an early 80s rendition of an old man's head floating in a big ornate orange tank, very surreal.
I liked this book enough, but it didn't strike me as Heinlein's best. His occasionally preaching tone seemed to come through much more often in this book than his others - you know what I mean, the lectures about rugged individualism and the like that he goes off on with alarming regularity.
I think my biggest complaint with the book was the (in my opinion) unconvincing portrayal of how a woman in the near future may think. I thought he did a pretty good job with some of his other major female protagonists (Friday in particular, but also Podkayne of Mars), but in this book I was not convinced at all that the thoughts he was putting into Johan and Eunice's 'mind' were believable.
He seems to think that a strong case of nymphomania should be normal in all women, and I just don't get it...
I sometimes take issue with Heinlein's views on sex, and his opinions of the female of the species seem to swing wildly between highly commendable and deeply paternalistic and misogynistic.
Another, more minor (sort-of) complaint that I have with his writing is that more often with his later books the ending seems to disappear. This is a great example of there not seeming to be much of a point to much of the last third of the book. Our protagonist struggles through dealing with the death of his most trusted aide, the shock that he now resides within her body, the adjustment to a 'female' way of thinking, proving to the courts that he is indeed Johann, and then it all seems to tail off into a yarn about manipulating his elderly love into marrying him.
And then it just stops! Are we supposed to assume from the final words that the three minds inhabiting Eunice's dying body (Johann, Jake, and Eunice) are all going to hitch a ride with the newborn baby?
If so, does this remind you of Being John Malkovich at all?