Say I drop a sword in my Breezehome and carefully position it to my liking on the table/bed/whatever. After that I save. Sometimes later I load and the sword end up totally elsewhere than I positioned it.

Not only sword's affected by that, pretty much anything is. What goes? And how can I prevent that?

Don't drop your items.

Position the item in question. Then leave Breezehome and reenter. If the item is on the floor, reposition it. Now leave and reenter again. Nine out of ten times the itme will now be a good boy and stay where you left it.

Also, I found that some items just outright refused to stay put, no matter what.. For example, I could never get my Mage's Circlet to stay on a shelf.

I believe the trick is to drop an item and then leave the house. Return to the house and then place it. It should remain where you placed it. I can't say I tested this yet. Heard you could do it and saw pics of a dibella shrine someone had made on a table.