Got it to work...
I finally got everything to work across all my devices (Kindle, iPad, Android and Mac).
This only way I can get it to work is if I do these steps:
1. Convert your book to mobi with Calibre (even if the book already is in mobi).
2. Edit the ASIN (113) field using an editor of choice (mobi2mobi, MobiMetaEditor). You might be able to use any valid ASIN or ISBN-10 (not ISBN-13) number, but I use the proper values from Amazon. ASIN if there's a Kindle version available, otherwise ISBN-10.
3. Send the book to selected devices (\Library\ebooks for Kindle), not via iTunes.
I have no idea what makes this work, but Calibre sets the 113-field in hex (it seems) and syncing only works with a B00-number or ten digits.
I'm fairly new to Calibre so there might be some way to change its setting so these extra steps won't be necessary, but... as long as it works for me, I'm happy. I read on my Kindle during the days, iPad when in bed, and iPad/android when I'm out and about.
Oh, all my I have transferred so far (about 30) have had correct ISBN and ASIN or ISBN-10 ( as amazon: ).