This spell creates an Invisible, Stupid, Shapeless Medium Force that performs simple tasks at your command until the end of the spell.
The spell does not say that it's about one creature or another being able to take action. Things do what they say they do. Note that the Find Familiar spell indicates that the thing invoked can take action.
Your familiar acts act independently of you, but he always obeys your orders. In combat, he launches his own initiative and acts in turn. A pet can not attack, but it can take other actions as usual.
However, the familiar is able to do simple tasks as a human servant:
Once on each of your tricks as a bonus action, you can mentally command the servant to move more than 15 feet and interact with an object. The servant can perform simple tasks like a human servant, such as fetching things, cleaning, mending, folding clothes, lighting fires, serving food and pouring wine. Once you have given the command, the server runs the job to the best of its ability until it finishes, and then waits for your next command.
I would say that dropping dishes is something the servants do, and that it is essentially instantaneous (no hesitation, because the servant is without spirit). This should be able to occur during the bonus action on the player's turn unless otherwise (ie the activity takes too much time).
Causing a distraction by dropping plates is certainly something that the servant should be able to do during the player's bonus action. However, as a DM, you decide what will happen next. When I'm DM, I personally use the rule of freshness – in this case, I'd probably grant a saveship of wisdom or intelligence control of the creature (to an appropriate distribution center ) on the first set of plates, then I would ignore future sets or with advantage. If the player starts to run with stacks of dishes otherwise, remind them that the dishes cost gold and that people do not like their dishes to be stolen.