I have been a Doctor Who fan since 2005. I had great hopes for seasons 5 and 6, because Steven Moffat had become the producer and lead writer. Moffat wrote my 2 favorite stories (2-part episodes counting as 1 story) from the Russell Davies series of 2005-2009, and all 4 of his earlier stories ranked among my all-time top 12 for the modern and classic series combined. Unfortunately, the first two Moffat seasons did not live up to my expectations, for several reasons.
Concept of the show: The 4 Moffat stories from the Russell Davies era conformed to Davies' conception of the show and the character of the Doctor. Davies viewed Doctor Who as a science fiction show, a la Star Trek. Moffat views Doctor Who as a fairy tale. I prefer science fiction. Both of the Davies incarnations of the Doctor - Christopher Eccleston and David Tennant - were serious characters. Eccleston played the Doctor as intense, enigmatic, very lonely, self-doubting, and angry over the total destruction of his fellow Time Lords in the Time War. In his David Tennant incarnation, the Doctor largely got over his anger, but his seemingly light-hearted banter covered up a deep loneliness and sadness, combined with steely determination. In his current incarnation, the Doctor is just silly and undignified - a madman with a blue box. Also, in his interactions with his primary companion - Amy Pond - he comes across as hen-pecked. Good grief! Also, the repeated "Hello sweetie" stuff with River Song has become tiresome. Many jokes are only funny once. I must say, however, that the silliness of the Smith Doctor has been declining in recent episodes.
Quantity versus quality: During the Russell Davies era, Moffat wrote a total of 4 stories and 6 weekly installments. Moffat is currently writing about 5 weekly installments per year for Doctor Who, plus a couple more for his other show (Sherlock), and is acting as producer for both shows. This does not allow him to devote enough time to each episode that he writes. Moffat needs to cut his number of weekly installments to about 4 per year (for both shows combined) and recruit better writers (see below) to generate the remainder of the episodes.
Inferior "secondary" writers: In my opinion, the following writers accounted for the top 10 stories from the Russell Davies era: Steven Moffat (4, out of the 4 he wrote), Paul Cornell (2, out of 2), Davies (2, out of 25 (31 weekly installments)), Robert Shearman (1, out of 1), and Toby Whithouse (1, out of 1). Stories number 11 through 15 came from Russell Davies (4) and Matt Jones (1, out of 1). (However, Davies might have written better stories had he confined himself to fewer episodes per year.) Whithouse provided 1 weekly installment per year in seasons 5-6; Cornell, Davies, Shearman, and Jones combined for ZERO. Moffat should recruit some of the other good writers from 2005-2009 and get Neil Gaiman (see below) to write more than 1 weekly installment next year.
Fixation with time-loop paradoxes: Moffat's first story - The Empty Child/The Doctor Dances - was a superb example of the "Doctor solving a problem" type of story. Moffat's other three stories from the 2005-2009 series all dealt with time-loop paradoxes. These episodes all worked well, especially "Blink," but this was partially because such episodes were "different." Having such episodes account for the bulk of a season, as they do now, is tedious and confusing. How much of season 5 actually happened after the last episode erased most of the season? Will the same thing happen at the end of season 6?
General tone of the season 6: Season 6 is darker and scarier than earlier seasons, and has more emphasis on morally complex or ambiguous themes (e.g., Amy's continuing interest in the Doctor even though she is married to Rory). Also, the Doctor seems perfectly willing to let River Song shoot people/monsters, whereas earlier incarnations of the Doctor were gun-shy (except for Christopher Eccleston when he encountered Daleks).
Specific episodes from the first half of season 6: 1) The Impossible Astronaut/Day of the Moon. This is a genuinely creepy story, Moffat's best since the David Tennant era (Silence in the Library/Forest of the Dead). Despite my general unease about "time paradox" stories, this one has an ingenious "time loop" plot twist at the beginning (which I will not reveal). Also, the aliens are a scary new enemy - will they be back? I disliked a couple of things about the story, which prevented me from putting it in my all-time top 10. First, I really hated it when River Song shot the Doctor's Stetson hat off. This was supposed to be funny, but I found it merely stupid. Second, former president Richard Nixon played a significant role in the story, and was portrayed very poorly. The actor did not look like Nixon, did not sound like Nixon, and captured nothing of Nixon's character. He was just a "generic president." 2) The Curse of the Black Spot. This was a silly 18th century pirate episode, loosely inspired by Pirates of the Caribbean, but without Johnny Depp. This is right down there with "Victory of the Daleks" as the worst story of the Moffat era. 3) The Doctor's Wife. This is the best story written by anyone other than Moffat since Human Nature/Family of Blood (Paul Cornell) back in season three of the Davies era. This is a clever story where the soul of the Tardis inhabits the body of a woman. Hopefully, Neil Gaiman will write two or three weekly installments next year. 4) The Rebel Flesh/The Almost People. This is a surprisingly good - and thought provoking - story about the nature of humanity and slavery. Much like the movie Blade Runner, it deals with artificially created human-like beings that are exploited. 5) A Good Man Goes to War. This is part one of a two-part story. This is one of Moffat's worst episodes. It is much too fast-paced and confusing, and provides little understanding of what is going on or why. It might have made a good 2-part episode or 90-minute special. It also gives away the secret of River Song's true identity. It probably would have been better to keep the secret until part 2 of this episode debuts later.