Other mistake: When Mr. Thursday goes to see Vastra, to hire her to investigate his brother's death, he doesn't see her face (she's a Silurian "lizard woman from the dawn of time") until she lifts her veil to take a closer look at a photograph he brought her, upon which he faints. However, Vastra's veil is quite see-through, enough that her non-human appearance is obvious to the audience even before she lifts it. The same thing happens when she goes to visit the coroner later - although he doesn't faint.
Other mistake: Billie Piper is listed as playing "Rose" in the closing credits. Rose was certainly mentioned, yes, but Piper in this episode was actually sentient superweapon the Moment, who merely took Rose's form, and was in all other respects nothing like the former companion.