I actually love the new series (David Tennant is my fav there) and if you ever watched the original episodes (I did years ago) the new imagining of it is quite--dare I say--"Brilliant".
About the "Mary Sue" comparison--yeah, somewhat--but in defense of the series, they are taking characters and ideas from the original series that everyone loved and highlighting them.
There is a lot of nostalgia there--especially for Brits--and I thought they did a great job of taking some absurd villains originally presented as nearly all styrofoam and cardboard props and bringing them forward without losing the charm of the original.
I'd also note that the Doctor has had to deal with much darker issues than those of the past and it hasn't all been wine and roses for him. He's failed on several occasions and people have lost their lives. The series is still intended for children (as well as adults) and I think they have struck a good balance so far. If I had seen "Blink" (the "Weeping Angels" episode) at eight years of age I wouldn't have slept again until I was 16.
I thought the Weeping Angels and the Silence were brilliant ideas for creepy bad guys (though a bit similar unfortunately) My favorite episode is "The Doctor's Wife" just because its always been obvious that the one constant relationship the Doctor has and can't live without is his TARDIS.
What really strikes me is that for British citizens, the Doctor is an iconic representation of what Britain's want to believe about themselves. The reverence and devotion to the show by Brits is actually really touching to see and I think it's wonderful that young people growing up can see something that reflects national pride and an encouraging view of the future and science.
I laughed watching a BBC talk show with an American guest and when he quipped that Daleks looked "cheesy and fake" and "weren't scary at all", the audience came to their feet and booed him. It was epic.
Derek Jacobi's reprise of "The Master" in "Utopia" was really well done.When he turned back to the Master from "The Professor" just did an awesome job of looking genuinely evil.
I just finished re-watching all the newer episodes--hence the reply. I'm actually going to see Fright Night just to see David Tennant do something else. In theory, the Doctor should only have two more incarnations. Will be interesting to see what happens.