A few days ago, after the Battle of Kvatch, I head to Cloud Ruler Temple and decide to use that as a temporary place to store items. I come back a few days later to collect my Mortar and Pestle, and realize that everything I put in that chest was gone, replaced with a few miscellaneous items.

I didn't lose much, but I would like to know what the guidelines are for placing objects in chests. I bought a cheap house at the Waterfront, and put my stuff there. Will my stuff disappear there too?

It seems you ran into an unsafe container. Many containers in the game world are unsafe, meaning that their contents will respawn if you leave them for 3 game days. The containers in the houses you buy should be safe though.

If you are not sure whether a container is safe you can test it. Place an arrow in it then go to another cell. For example if you want to check the containers in your shack you should go outside. Wait for 72 hours and go back. If the arrow is still there the container is safe.

Additionally, if you just drop items on the ground, they will never disappear. Weapons might get picked up if an NPC without a weapon goes into combat though. Not too likely to happen in most situations, however.

Your items will be safe in all of the containers in your Waterfront house.

It never happened to me, but I heard that tiems can sometimes fall through the floor. So if you have a safe container it's better to put them in there, just in case.

I use a portable sack from a campsite mod that is usually left on the ground while camping.
It falls through the floor 90% of the time. I have to TCL and dive deep underground just to retrieve it....