This is the first time outside of mini-episodes that River has been in a story not to feature one of the Doctor's companions alongside her and the Doctor.
Any tiny hint of what species he might be?
Nardole: I dunno.
The Doctor: Okay, never mind. You just stay there.
The Doctor: You're probably going to need a mop.
In her first appearance in the series, River questions the Tenth Doctor about the crash of the Byzantium, an adventure she shared with the Eleventh Doctor. While this makes sense if she is mistaking the Tenth Doctor for a Twelfth or later incarnation, her photo collection in this story has all of the prior Doctors in chronological order. This, coupled with her insistence that the photos are the only incarnations of the Doctor, implies that she does know the correct order, and therefore would also know that the Tenth Doctor would have no memory of the Byzantium.
Changes to the opening credits were made for this Christmas time episode. There are added snowstorm effects that the Tardis flies through and in addition the circling 'planets' (visible just after the Alex Kingston credit) are in fact Christmas ornaments.