This Photo looks like Artex Stipple Finish to me !!!
I thought that at first but, as the OP says it's a re-skim, thought it must be the plaster, although it really does look like a lightly textured paint/Artex finish.
My assumption is that the paint was applied heavily with a medium pile roller and not rolled well enough before drying - I've seen it countless times from DIYer's and, sadly, a number of pros.
Back to the overall job:
I think 1½ days is pretty quick for a freshly skimmed room, even without knowing the full size and layout, which suggests no real prep was undertaken and some paint was just slapped on to cover everything. The blemishes spotted by opps are pretty common after skimming as plasterers can't always get a perfectly flat finish along skirtings/architraves/corners. This is where a good decorator will spend time filling and sanding to achieve the best possible finish. If you were happy with the plaster finish and didn't specify any filling, then I can understand why it wasn't addressed, but that doesn't seem to be your gripe. You are more concerned with the actual paint finish which, as stated by everyone here, can only be classed as poor, at the very best. It can be remedied with sanding and re-painting but, the question is, who bears the financial burden? A guy who has spent just a day and a half painting a room out isn't going to want to spend another day and a half rectifying things free of charge, even if he realises he has done a pretty bad job. you could come to a compromise, as suggested earlier, and ask for it to be re-finished to a higher standard at a lower price, but I think you will be 'politely' turned down.
IMO, you have got the finish that is expected with the time taken and the price. Would you have been happier to have paid double to get a much better quality finish, or were you happy with a timescale and price set out beforehand? Understandably, either way, you would have wanted a better finish, and that is where 'chalking it up to experience', like opps says, comes into play. At least next time you'll know that you don't get a quality job for such a low price in such a quick time.
Hopefully it gets sorted one way or another but, other than what has been said, I don't think much more can be offered.
Good luck.