They definitely catch most of it. Like people. there are dumb dogs.
I can take my dog Chuck, point at a box, say Chuck, get in the box and he knows what to do. He knows from my tone that I am telling him to do something. He knows I want HIM to do it and I am pointing at the box. Clearly he might misunderstand until he gets an idea of what he could do with said box but I am always amazed he figures out 90-95% of what I am trying to get through to him. You are absolutely right, they are fantastic at context clues.
(Chuck Norris, Dog: I can get him to point at a box and say my name and then when I jump in the box, bro gives me a cookie. He’s really smart. He can point, speak AND get the cookie jar open.)
We’ve kept dogs as companions for around 10,000 years for a reason.