Broken Base: The fandom creamed this episode in a popularity poll taken in Doctor Who Magazine. Lowest-ranked overall out of any Eleventh Doctor stories at the time, and one of the lowest on the list, period.
In particular, the leaf scene in the climax has been rather...controversial with fans. Some argue it's a powerful scene that was set up well, gives Clara's character a chance to shine and fully showcases her heart for the first time (which we'd be seeing a lot more of the following season); others argue that it's a Tastes Like Diabetes ending (in an already sugary sweet episode) which completely undercuts the Doctor's epic speech moments earlier.
Continuity Lock-Out: The Doctor's casual mention of having a granddaughter threw some viewers unfamiliar with the Classic Series for a loop, as it was the first explicit reference to Susan Foreman in the revived series at that point.
Crowning Moment of Awesome / Crowning Music of Awesome: The two climatic scenes where the Doctor and Clara bare their souls to the Old God to defeat him - the Doctor by deriding the parasite and letting him feast on his memories, and Clara by giving up the most priceless heirloom and memory she has of her late mother - both of which are backed by some of Murray Gold's best music, "The Long Song" and "Infinite Potential".
Ham and Cheese: The story is incredibly cornball to many, but there is a beauty in watching the Doctor give an oratory assault on a flaming ball of doom. Even the episode's detractors point to Matt Smith's "Akhaten Speech" as one of his best performances.
Special Effect Failure: In the scene where Clara and her dad are standing on her mother's grave, they didn't bother to use any makeup to age him, so he looks exactly the same as in the scenes set in the 1980s except for some gray colour in his hair.