I agree. If my steak came out grey rather than my preferred dripping pink, that is obviously the kitchen's mistake and the server should not be held accountable (unless he/she refuses to return the item).We don't know if the server put the order in or simply forgot to. Again, to me, the big problem is the customer had to tell the waiter there was a problem.
I agree with the OP on the messed up drink. If that happened on it's own, no big deal, not worth complaining about. On top of everything else, it adds another problem to a bad experience.
And no, the server is not always the problem. However, they are the "face" customers see and are responsible for getting things right. If a cook makes a steak well done when you ordered medium rare, do you go back to the kitchen and complain? No, you tell your waiter, and they "make it right".
However, not noticing that your customer is sitting at their table without food is the server's job and it is the server's responsibility to figure out why there is no food.
Problem solving and then telling the customer what happened would earn the tip. Ignoring it till the customer brings it up and then blaming somebody else; sorry, no tip.
I have worked corporate, commissioned sales. It was my job to stay on top of all aspects of the sale to make sure the sale went through. As the link to all the departments involved, it was my job to follow up continuously to make sure all the pieces fell in place for the customer. If the sale did not happen, no commission. My boss would not come to me and say "Oh sorry, you were too busy to follow up on that sale, but we will give you the commission anyway."
Mistakes in life can sometimes cost you. One thing, you rarely make that mistake again.