1. The characterisation. Seriously, one of the reasons The Three Musketeers has been so frequently adapted is because of the simple, easy-to-understand characterisation of the main characters: there's the Romantic One, the Angry One, and the One of Prodigious Appetites, plus the Naive and Innocent One. The fact that the series itself regularly became confused over which one was Romantic, Be-Appetited or Angry, with all three Musketeers being all three at all times, is a real problem.
2. Race. I was really happy when I saw that Porthos was played by a black actor-- it's a nice nod to the fact that Alexandre Dumas was himself black, as well as acknowledging that not everyone in pre-industrial Europe was white. However, because the series was filmed in Croatia, all of the extras were white-- and so was 99% of the guest cast (apart from a cameo by Ashley Waters), meaning that for 9 out of 10 episodes, Porthos appears to be almost the only black person in France, and no one appears to notice. And the 10th? That's the horribly patronising one about the slave trade. Which brings me on to...
3) Historical accuracy (lack of). Yes, I know it's a drama, and that dramas take liberties with historical facts. But this one's connection to history is so tenuous it might as well be set in Ruritania as in France. The abovementioned slave-trade episode is particularly egregious (17th-century France has no major colonies? That's news to any Canadian raised on stories of the coureurs de bois and the Jesuit missions), but it's far from the only offender.
4) Familiarity. 17th-century France is a pretty strange place by modern standards, a society with very different ideas about legitimate governance, the value of life, the place of religion, marital fidelity, and science. This is a popular drama so I'm not expecting Hawksmoor, but it can't be impossible to nonetheless give an idea of the foreignness of the past-- hell, even the likes of Poldark managed it better. Just to give an example: at one point a character exclaims, "I'm a citizen of France! I have rights!" to which someone ought to have responded "No, on both counts, for at least another 150 years." ETA: Even more inexcusable when you consider that Game of Thrones is set in a society with child marriage, eunuchs, polytheism, and a royal family with a rather liberal attitude towards incest, and yet doesn't seem to have alienated its audience one bit.
5) Repetition. Someone is accused of a crime they didn't commit. But it's actually all a ruse to entrap someone else. Lather, rinse, repeat. The series is only 10 episodes long, for heaven's sake!
Good points: Peter Capaldi, of course; the characterisation of Louis XIII was a lot subtler than I was expecting, and yes, they did find some pretty palaces to film in (even if those shots of the painted ceilings did get old rather fast). For the first few episodes it was fun to do a counterfactual reading of the series in which the Cardinal is actually the hero and the Musketeers the villains, though that did get boring eventually.