The good bits first. Catherine Tate is fantastic in this episode, which is all about the potential of Donna Noble, an ordinary person, to change the world. Donna is one of the best Who companions ever, as white_hart has explained much more eloquently than I can. This is the third Doctor-lite episode of New Who, and the first to use the format to showcase the companion's story. It is impossible to imagine Rose or Martha bearing the same weight of narrative. (Jack and Sarah Jane get their own spinoff series, but both of course are older characters.)
The second good thing about the story is the portrayal of post-apocalypse Britain. I have written before about politics in parallel universes. Here we slip much more to the Inferno model, as mass destruction leads the government to abolish civil liberties and set up concentration camps for the non-English. The great thing about this story is that it does so much to convey what this soty is like with surprisingly little material. Bernard Cribbins' silent look of tearful horror as the Italians are taken away says more than paragraphs of exposition could do.
I am neutral about the episode's use of the point of departure concept. New Who has tackled this several times Father's Day in 2004, and not one but two Sarah Jane Adventures. So I am not wowed by the audacity of the concept; it is almost routine. Also I can't help but notice that Pete Tyler, parallel Donna and Sarah Jane's parents all choose to die in car accidents - Pete and Donna both throw themselves under the wheels of a passing vehicle as Rose watches. The best treatment of the point of departure I have seen (and that's not saying much) is in the movie Sliding Doors, which cuts between the two realities. Doctor Who has yet to do a really interesting spin on it; Time Beetles are not the answer.
Not to be too negative on this point: what we are being asked to imagine is the Doctor's world without the Doctor, where the Thames was drained, the Titanic crashed on Buckingham Palace, millions of people disintegrated into fat and the Sontarans almost poisoned the rest (though on the flip side, presumably Professor Yana will live out his life as a human and die at a ripe old age without ever realising his origin, so Harold Saxon never appeared on the political scene). Big Finish did an excellent similar story where the Brigadier has retired to Hong Kong after failing to deal with the series of alien invasions in the 1970s, and is confronted years later both by the new Doctor (played by David Warner) and by the new head of UNIT (played by one David Tennant).
My big problem with this story can be summed up in one word: Rose. It is not just Billie Piper, whose performance and particularly diction in this episode are respectively monotonic and peculiar. Did she have a cold? Was she recovering from dental treatment? I neither know not particularly care.
But the original point of Rose is that she is an ordinary girl caught up in extraordinary things, and the Rose of Turn Left has lost that. I am not one of the legion of Rose-haters among Who fans: I thought that she injected the new love-interest theme into the old companion routine very well, and made us care about her and her fate. Now she returns as a grim dimension-hopping superwoman who for some reason cannot say her own name. She never smiles (and Billie Piper has a very disarming smile). Think of the Rose / Sarah Jane and Donna / Martha encounters, and then consider the total lack of chemistry between the two leads in this episode. I don't blame Piper; she has done her best with confusing and shallow material. But I find the Rose parts of Turn Left almost unwatchable.
I'll also note, as others have done, that the opening sequence has the most offensive Chinese stereotypes in Doctor Who since Talons of Weng-Chiang.
I feel pretty certain that I will rank Turn Left behind the Moffatt two-parter on my ballot. (For a slightly different take, see ibishtar's excellent summary.) I wonder if others will react the same way. The guts of my objection are to the use of Rose as a character; for viewers who know nothing about her, I imagine this would work rather well as a Who treatment of a familiar sfnal theme, with a strong performance from the central character and some interesting thoughts about alternative history. Your mileage may vary.