Roots: Cromwell's comment (see: Dialogue Triumphs) suggests an awareness of the longevity of his "warts and all" portrait declaration. Ace mentions The Wizard of Oz (see: Continuity)
Dialogue Triumphs: Cromwell: "It's the warts, isn't it? Yes, everybody's heard about the warts!"
Continuity: The TARDIS Library has lemon trees in it (as encountered by Hex), near the Doctor's collection of Ladybird books. It is a huge room, and Ace says the Doctor swears that he has read its entire collection - she on the other hand is distrustful of 'readers', having been out with one before. The TARDIS kitchen is to the left of one of the several mezzanines about the ship - it has a toaster, but no milk. There is a jar of ointment in the console room. Hex finds a large room containing an area of open wilderness, including a range of mountains (Ace says they can be climbed, and that she successfully scaled the largest there) - it has a degree of wind in its atmosphere.
Ace says she got her name because her mother was a fan of The Wizard of Oz - as is the Doctor. She doesn't know how to make loose-leaf tea. She is an accomplished sword fencer (see: Untelevised Adventures). She implies that she has some knowledge of how to set the TARDIS's coordinates for specific location (in this instance South Croydon, 1990). Her decision to use Ace as her name ("short for Elizabeth") in this story is perhaps wise, given that McShane would draw understandably negative attention; nevertheless the latter name is not mentioned at all, suggesting that she has retired the alternative moniker.
Hex kills in this story, and is badly shaken by the experience of it and of war in general. His attraction to Ace continues, and is noted by Ace herself (but not reciprocated as she responds to him fraternally). A good deal of his knowledge of Cromwell's atrocities in Ireland came via his grandmother's stories. He stayed in a study hall whist at university.
The Doctor has brought Ace and Hex to this point in time specifically to test Hex's ability to recognise places in history by the environment around him
Untelevised Adventures: Ace says she learned everything she knows about fencing (and how to make "a mean fig casserole") from the Captain of Cleopatra's Guard - "a friend of a friend". She also later names Julius Caesar, Lord Nelson (see: Links) and William Tell as examples of people the Doctor namedrops on the presumption that he has met them. Confirmed among these (by physical evidence of a name tag) is Peter Chamberlen, inventor of the obstetric forceps.
Links: The Doctor apparently did meet Lord Nelson, as evidenced in The Stuff of Nightmares. The 'wilderness room' within the TARDIS may be the same as that which appears in Three's a Crowd. Ace's apparent fencing training by Cleopatra's bodyguard mirrors that of the Doctor's in Masque of Mandragora. Ace asks Hex if the Doctor has given his "you can't change history" speech yet (The Aztecs).
Location: Drogheda and Wexford, Ireland 1649.
The Bottom Line: "Been in the wars have we?"