Abbreviations:
HOUN = The Hound of the Baskervilles, the original story by ACD
Episode 2: The Hounds of Baskerville (HB)
Both HB and HOUN are set in Dartmoor, near Princetown prison. In HOUN, this was a plot point because a convict recently escaped; in HB, it's referred to only in passing by the bartender's partner as something that makes it difficult to sleep at night.
In HB, Sherlock at first acts as though he is going to send John to Dartmoor alone while he takes care of business in London. In HOUN he carried through with this, then went to Dartmoor secretly.
In HB, the dramatic daytime view of Sherlock standing atop the rocks corresponds to 'the man on the tor' nighttime scene in HOUN.
In HB, Baskerville Hall has been replaced by the Baskerville research facility. The Great Grimpen Minefield corresponds to the Great Grimpen Mire in HOUN; in both versions, it's the location and the means of the main villain's death.
Mrs Hudson in HB is being courted by Mr Chatterjee, who turns out to be a bigamist. In HOUN, both of the Stapletons (in reality a married couple) pretended to be single, and each became seriously involved in a dating relationship with someone else as part of Stapleton's plans. (He courted Laura Lyons under false pretenses, while she did the same with Sir Henry.)
The client in HB is Henry Knight; in HOUN it was Sir Henry Baskerville. (Dropping the title and using the surname 'Knight' is a nice touch.) In both versions, he's a wealthy man, and concerned about the suspicious death of an older male relative.
Dr Mortimer in HB is Henry's therapist. In HOUN, Dr Mortimer was the local GP, but after Sir Henry's breakdown at the end of the story, spent a great deal of time travelling with him and looking after him.
In HB, Henry goes to 221B himself; in HOUN, Dr Mortimer went. In both stories, the supposed story of the hound is given to Holmes, who is inclined to dismiss the superstitious aspects. The 'footprints of a gigantic hound' speech is taken directly from HOUN.
At Baskerville -
- Corporal Lyons corresponds to Laura Lyons in the original, but in this story is fooled by John and Sherlock, whereas the original character was used as a catspaw by the villain and was told the truth by Holmes.
- Dr Frankland in HB corresponds to the local landowner Frankland in the original, who disowned his daughter Laura Lyons upon her marriage. He's treated as a harmless eccentric in HOUN, but behaved very shabbily toward his daughter, who badly needed help to be able to set herself up to be able to earn a living but had to get that help from other people (e.g. the first murder victim in the story). In HB, his eccentricity is actually a dangerous obsession with trying to make a very dangerous chemical weapons research project pan out.
- Major Barrymore replaces Mr and Mrs Barrymore, who in the original story saw to the running of Baskerville Hall.
- Dr Stapleton replaces the Stapletons in the original (the villain and his wife, who was posing as his sister). Like the original Stapleton, she makes an animal glow in the dark, but in this case via genetic engineering rather than phosphorous.
In HB, Sherlock's cover story about having a bet with John, and using it to get information out of someone at the pub, corresponds to a similar tactic used in "The Adventure of the Blue Carbuncle." (As in the Granada TV adaptation, we're actually shown that the bet was paid up on the spot.)
The light on the moor that John mistakes for Morse signals in HB was, in HOUN, a set of signals between an escaped convict and the family members who were helping him - that is, what John mistakenly thought were signals in HB really were signals in HOUN. (Similar reversals happened for the 'Rache' clue in ASiP and for the poisoning in the 'Speckled Blonde' case on John's blog).
Sherlock's 'grit on the lens' speech corresponds to a similar comparison to the effects of emotion in "A Scandal in Bohemia".
The 'conductor of light' speech in the churchyard is taken from HOUN, although in that story it occurs near the beginning.
In HB, Lestrade helps John and Sherlock on his own time, particularly during the endgame. In HOUN, Lestrade likewise acted as backup during the endgame, although it was never explained how the jurisdiction problem was addressed.