While this solution doesn't address the problems of button batteries while in use in everything from greeting cards to remote controls to toys, it does keep the old batteries corralled until they can be recycled or disposed of properly (call your local solid waste district or trash service for more information).
We drop our dead batteries in a child-safe vitamin container, and put the containers out of the kids' reach. I relabel the containers solely for my own amusement (Do you do this? Maybe we should start a Pinterest board).
The filled container is deposited at our wonderful local recycling facility (which accepts a broad array of batteries in a co-mingled bin).
Not only does this hack keep our batteries away from our little kids and out of the solid waste stream, it also means that batteries outside the bottles are easily identifiable as fresh.
***Baby Toolkit is a frontrunner in observing the obvious and the ridiculous in parenting. It is written by two geek parents presently enjoying a Fall-like Spring somewhere slightly above the Mason-Dixon line. Although we make no links in this post, we are admittedly Amazon affiliates, so a portion of purchases made through our Amazon links fuel our pipe dreams of owning a bathtub with a water slide (thank you!). Our actual voices (and sordid secrets) can be heard on our board gaming podcast GreatBigTable.com.