Replacing Carpet with Hardwood floor - contractor issues on base board cutting
If your baseboard goes down to the subfloor then I would be very surprised that the installer took the time to cut into it so that hardwood would go under it. If the contractor has a specialty tool for this which makes the endeavor take seconds instead of using an oscillating multi-tool then that would be cool.
Anyways, the baseboard was probably cut unevenly so brand new shoe molding is designed explicitly to hide the imperfections where your floor meets the baseboard; regardless of whether the floor goes under the baseboard or butts up right against it.
What exactly is the issue if hidden drywall was damaged a little bit?
In your mind what exactly would make things right or better? Based on your worries &quot;making it right&quot; is going to be expensive.
Overall, the install looks fairly proper. Patch the holes and add a fresh coat of paint on your baseboard and shoe molding and it will look great.