On loading day, make sure everything is listed on the inventory and that you agree with the descriptions. If you don't agree, make a note on the inventory, and secure a signed copy. Before the van leaves, walk through the house to make sure everything is loaded. This is your responsibility. Once they leave, few moving companies will turn around for something left behind.
Most movers are ethical and honest.
They want to provide you with a good move, as much as you want one. The answer usually will be pretty direct. Inventories are most important when your goods are going in storage, you are moving overseas, or you know your origin and delivery crews will be different. If there are any problems, few can argue with a signed, documented list. Used under License.