Skirting board cuts/quality what is “good enough”

the project manager should ensure that the foreman ensures all the trades are working together and in a clean and safe manner. the standard of work should be paramount with all cuts and joints done neatly using industry standard techniques that and joiner will posses.

Personally no that's not good enough, if installed adequately you wouldn't have this problem and now you'll need extra work or a delay to the project to get it up to standard and as for the cleanliness the site should be kept to a safe and workable manner and upmost to keep your safety in mind.

It sounds like these builders are not taking the care that you are expecting of them to do a proper job. They may use large quantities of caulk to smooth out the corners and joins and it may look acceptable after or it may not, that is for you to decide. For me as a carpenter I wouldn’t dream of asking a customer to accept anything short of excellent work, always.

I think this would need more context to give a proper answer. With regard to the skirting, if the quality is unacceptable, then it needs to be rectified to a standard befitting of a proper carpenter/joiner - a PM isn't required for that standard to be set, you as the customer can do this. The house being like a bomb site is a common complaint when builders are undertaking work but this should be kept to a minimum and the disruption kept to a minimum - wall removals etc is messy work but it will make your house look like a bomb site but unavoidable in some cases. This is the role of the PM to ensure trade co-ordination and liaison of trades is paramount on jobs such as the latter.