Here are some pics.

Why did you have your floors done after painting baseboards? They always get banged up and from what I know is listed in most contracts that the floor finisher is not responsible for this type of damage.

Don't mind the bottom, we are getting new shoemolding but halfway up baseboard, it's not going to cover that huge scrape.

@millworkman Our flooring company actually advised us to do paint first. He said if they scruff up paint will be easier to touch up than if the painters got paint on the updated floors.

Its all fixable, with sanding, filling in all dents etc, and sanding some more and a complete repaint job. This is a bit beyond touch up stage. Yes, the floors should have been done before the trim was painted. Thats what tarps or paper laid on the floors and taped is for. Thats, exactly what will have to be done now. That prevents paint from getting on your newly done floor.

Door is floor guys fault. They crashed into it. But baseboards, that's all painters. Paint should scuff not peel. If, it peels like that, it's a clear indication, there was no washing to decontaminate or abrading for mechanical adhesion.

This happens with floor finish also. When we have to do a recoat. The floor needs a deep clean and a mechanical abrasion to prevent peeling.

Check your contract to see what you paid for.

Looks like the painters didn’t prep the baseboards properly. Did the use an oil based primer first and sand? You can’t just paint latex over what looks like a previously varnished trim and expect it to adhere.

Again, G&S has it exactly right.

Despite what your floor person said, the generally accepted practice is floor first, painting after. Walls are painted more often than floors are refinished, therefore painters must regularly work over finished floors without messing them up (unless they want to go out of business). OTOH floor refinishing uses multiple machines, stain and finish right next to trim, so it's illogical to expect nothing will happen to the trim.

They should compensate you for the ding on the casing and your painter should fix the rest.