This is ****. Sorry, I can't be more positive than that.
I've just installed a load of skirting - as a DIYer who has only done it once before, using consumer grade tools, in a 1950s house with walls about as straight as a banana - and it looked SIGNIFICANTLY better than this, even before caulking.
If I was paying a professional to do it, I would expect it to be done to a professional standard, not look like it was done by the work-experience kid after a few pints!! They should have caulked it at the very least (although even that would be a bodge job, as those cuts are very poor).
In the UK at least, you would need to give them a reasonable opportunity to sort it out (free of charge of course) before you can start looking at legal remedies, but I'd certainly be documenting everything, and withholding payment until you're happy with it.
This is exactly why I do all my own home renovation work (unless legally unable to do so, e.g. gas and major electrical work, or the costs of tools/equipment would be prohibitively/disproportionately high); I realise it's obviously not possible for everyone due to a variety of reasons, but from my experience, finding a decent tradesman who actually does a good job and takes pride in their work is the exception rather than the norm (anyone fresh out of school can buy an old van, spend £50 on some vinyl lettering, and call themselves a painter & decorator).
It might take a bit longer to get things done - due to needing to fit it around work & kids - but at least I know it will be done to a standard I'm happy with (and probably cheaper!)