I am also currently experiencing this problem. I can go into build/buy mode and can continue to play the game after going back to live mode, but cannot interact with anything from my fridge as it gets stuck again. I have to completely quit the game, and every time I go back in I can only take a few items before it does this again. Clicking on an empty space does not help fix it, I have to completely leave the game.
You can avoid much of this by taking things out of the storage units and putting them out into the world first before putting them into your sim's inventory. For example click on the wrapped meat and then select one of them and put it onto a counter or table, Then do the same for as many as you need. It takes longer, but you avoid the sticking issue. Also after going into build mode, you can often do something such as dragging a plate or trash to the sink or trash can and that will allow you to once again select things without having to quit.
If you do quit, it is best to do so without saving.
