This episode has gained quite a polarizing reaction from the look of things. While I can understand why others don't like it, I personally found it to be an excellent episode.
This was a very serious episode with lots of emotion. Peter Capaldi and Jenna Coleman really got to shine and their final scene together in this episode actually got me a bit choked up due to the raw emotions that the two characters were showing. The small supporting cast was quite good. Ellis George portrays a realistically likable teenager in Courtney Woods and Hermione Norris gives a good performance as Lundvik.
The monsters in this episode had a great design and the curveballs this episode threw (more specifically the ones involving the Moon and the Doctor) were wonderfully unpredictable. Some of the twists and plot points do require quite a suspension of disbelief; but, in a show about an alien who travels around time and space in an old English phone box and changes his face and personality every so often, it wasn't that difficult for me to buy some of the stretches in scientific fact.
Overall, I found "Kill the Moon" to be a splendid episode with fantastic performances, lots of emotion, interesting twists, great cinematography, and excellent sound design. I'm definitely looking forward to seeing how Series 8 continues from here!