I'll be referring to & occasionally directly copying from Ariane DeVere's transcript, as my laziness only increases over time.
This may be edited. Please let me know if I missed anything or messed up somewhere. The actual cut bits for the dialogue will be in bold.
1) After Mrs. Hudson leaves 221B, and John says the line What the bloody hell was all that about? The following exchange is cut, and goes straight to Sherlock shouting ”I need a case!”:
SHERLOCK: You don’t understand.
JOHN: Go after her and apologize.
SHERLOCK: …apologize? Oh John, I envy you so much.
JOHN: …you envy me.
SHERLOCK: Your mind…it’s so placid, straightforward, barely used. Mine’s like an engine, racing out of control; a rocket tearing itself to pieces trapped on the launch pad.</i>
2) Inside Baskerville, after John asks ”So what exactly is it that you do here?”, the following exchange is cut:
CPL. LYONS: I thought you’d know, sir. This being an inspection.
JOHN: Well, I’m not an expert, am I?
3) After Cpl. Lyons introduces Dr. Stapleton. Dr. Stapleton asks ”Yes? …who’s this?” Those lines are cut.
4) After Sherlock and John leave Baskerville. There are two shots of the moor, then the entire scene with the two in the car (in which they discuss Kirsty and Dr. Stapleton) is cut, skipping straight to an exterior shot of Henry’s house.
5) When John copies down the Morse code on the moor. He whispers the letters slowly as he’s writing them. His repetition of the individual letters (”U, M, Q, R, A” is cut (skipping straight to him saying it as a word: “Umqra?”).
6) After Henry points out Dewar’s Hollow. A shot of John walking and loudly whispering ”Sherlock” is cut.
7) After they leave the moor (directly after Sherlock insists that he didn’t see anything) – the entire following scene at Henry’s house (including John trying to calm Henry and Henry insisting that they both saw the hound) is cut. It skips straight to John approaching the chairs by the fireplace.
8) After John leaves the pub to go after the flashing light. The entire following scene at Henry’s house (including Henry flashing back to the words “Liberty” and “In”) is cut. It skips straight to John back on the moor.
9) As they’re driving towards Baskerville – there is a montage of the animals/experiments, and then a shot of them driving towards the security gate. The following sections of dialogue (including the security guard asking them to turn their engine off, and Sherlock explaining what they’ll do when they get inside) are cut, instead cutting straight to the gate opening and them driving inside.
10) Additionally, after they drive past the gate into Baskerville, the following scene with Major Barrymore and Sherlock is cut. It skips instead to Henry’s house.
11) In the lab at Baskerville. When Sherlock opens the cage John is in, John says ”Jesus Christ, it was the hound!” The “Christ” was cut in the PBS airing. (Although later, when they encounter the hound at Dewar’s Hollow, Lestrade’s “Oh Christ” was kept in.)
12) During the “mind palace” scene. As Sherlock brings up the image of Elvis Presley and the words “Hound Dog” – the words that are sung (“You ain’t nothin-”) were muted for the PBS airing (presumably due to copyright issues).
The following are cuts to the nonverbal scenes, the length of a scene, or the transition of a scene. I'm only putting in significant cuts. For the purposes of these posts, I'm defining a significant cut as either the loss of a complete shot, or the cut of something that would have added something to the scene. Occasionally, a few seconds of an extended shot would be shaved off - I didn't count that here.
1) Extended scenes of them driving to Dartmoor are cut (a shot of John looking out the window, and a shot of the jeep driving away from the camera). Also, a bit of their driving up to the Cross Keys Pub is cut.
2) At the Cross Keys, after the scene with Henry and Dr. Mortimor. The shot of Sherlock walking into the pub is cut.
3) Small shots of them driving up to Baskerville are cut, as well as of them getting out of the car when they enter Baskerville. It cuts straight to the beginning of the shot in which Colonel Lyons drives up. A bit of them walking after John pulls rank was cut.
4) A few shots of them walking into the moor at night were cut.
5) A few shots of John walking around – directly before and during the time he hears the metallic thrumming sound - were cut.
6) A few shots of Sherlock walking up to John in the graveyard near Henry’s house were cut.
7) At the inn, as Lestrade is looking through the innkeepers’ paperwork. The shot of Sherlock stirring the tea and the two following shots (of John watching, and of Sherlock walking towards John) are cut. Additionally, after they leave, the shot of the innkeepers looking at each other is cut.
8) In the lab at Baskerville, after the bright lights flash on and the alarm starts blaring. Some shots of John trying to walk to the door are cut.
9) In Baskerville, after the scene of Henry shooting a mirror. The beginning of the shot, with a man in uniform walking out the door, is cut.
Cuts made to "A Scandal in Belgravia"