Table top needs to be 36-42" from the wall or any furniture on the wall to have room for chair scoot and sit space so I say no to the serving piece. My advice for a real update would be to get a rug under the table. It should be 4' larger than the table top. Remove the table cloth and the little items on the floor and walls left and right of the door and by the FP. Put the clock in the kitchen. Lower the sconces and art so the center point of the art if 5' above the floor and the sconces are centered just a bit below the center point of the art. Lower your chandelier to 36" or less above the table and remove the clutter from the fridge. I think there is a better more decorative solution for the wine storage, but without seeing what you have I can't be sure.

I've run into this situation before. The room is not wide enough for a normal serving table. I had one made that was only 8 1/2" wide 12" max, but it did required a wall bracket to keep it from tipping. In another case I made up a wall shelf unit 11.5 inches deep and 6' wide that hinged to the wall at the bottom. This acted as a serving shelf when flipped down and against the wall. Just locate the hinge at the table height. (use continuous hinge to connect the wall and the bottom of the wall boxed shelves)

You have enough room for something like this ,additional storage for your good dishes,trays and table cloths . Also consider to add some sort of treatment for the sliding door either a fabric vertical or panels .
You could move the table just a bit it doesn't look like its centered from what i'm looking at :) this will give you more room ....I think:)

Get out the painter's tape and tape off the area that will be taken up by the server table. If you do not have 24" between it and the table top you can't pull the chairs out and sit down without bumping into it.

Decoenthusiast: you gave great advice. I was thinking many of the same things...but you NAILED it.