Dr Watson's pipe?

Have a link to a pic?
Sorry, I tried to google pics of Watson's pipe from said show but came up empty. From your description it's a half-bent pipe of some kind.

The one in the first picture you posted is a Canadian. It might also be a Liverpool, but the shank looks more oval than round to me, ergo Canadian.
#2 is a half-bent bulldog. #3 is a squat bulldog; although it could also be argued that it's a hybrid of a straight bulldog (it has the bulldog's diamond-shaped shank) and a bullcap (due to the squat, large diameter bowl).

The consensus is that a diamond shank and a bowl with rings makes it a bulldog. If it has the rings and an oval/round shank that makes it a Rhodesian.
Now brace yourself, millions of opinions are coming lol.

Now brace yourself, millions of opinions are coming lol.

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We haven't had a good Rhodesian Vs Bulldog debate in a long time. :mrgreen: And so....

If it has the rings and an oval/round shank that makes it a Rhodesian.

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I don't believe it has to have the rings to be considered a Rhodesian, as long as the bowl shape is somewhat there... in other words, rounded down or angled down at the top of the bowl to where rings might be if the carver or maker decided to put them there.

Oval?? Are you referring to the picture of Nigel Bruce? I didn't post that image.
So if #3 is a squat bulldog, what is it that defines the diamond-shaped shank, then? When I did an image search for the 'Straight Rhodesian' most of the results showed this type of shank.

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Ooopsie, I scrolled too fast and didn't see it had been the Capt'n who posted the portrait of Mr Bruce holding a pipe with an oval shank larger than twice the height of the billiard-shaped bowl: i.e. the definition of the Canadian shape.
RE: the photos that you did post, Judcasper, what Lordofthepiperings said. To an avid classifier obsessed with exactitude, the definition of a bulldog shape requires the stem to have a diamond shape. It's like a car needing to have two doors in order to be a coupe; four doors would exclude it from the coupe category and force it into the sedan one.
Of course, you have to keep two things in mind:
1) Pipe shapes are an umbrella term, but carvers will introduce small variations. Just go to SPC's website and use their Pipe Locator to make a search for any given shape and you'll see myriad interpretations, but overall they all fit the same template that defines the shape.
2) There are pipers who don't give a flying trout about purism. They'll have their opinions and stick to them. I won't waste time arguing with them.

Addenda:

This pipe? Straight Bulldog.

I'm even more confused now as to why my image search for the Rhodesian brought up so many pipes with a diamond-shaped shank.

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Either people who don't know their shapes, or image makers and/or content uploaders just throwing in keywords willy nilly, or both.

image makers and/or content uploaders just throwing in keywords willy nilly

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So much this. Don't trust an image search. The pipe charts are the better option. Definitely a straight bulldog and from that image it has a silver shank accent. Many of the pipes used during that time were Peterson, so the one you search may very well be as well. And just for fun, Watson also smoked a square shanked version:

This and some of their related posts have a lot of research about these pipes already done.

Judcasper, the good news is that this shape and setup was incredibly popular at the time and you will have no problem finding a similar silver capped bulldog from the era. The bad news is that this shape and setup was incredibly popular at the time and you will likely have no luck discerning who made that particular version of this pipe.

The problem with this kind of debate is that the answer is usually fuzzy. In this case Nigel Bruce had many, many pipes.
A tobacco trade article from the 1940s states that of the five "notable" pipe collectors in Hollywood, Bruce ranked first. In case you're curious, the other four were John Ford, Archie Mayo, Jean Hersholt, and Arthur Hornblow (described as a less avid collector than Ford, Mayo, Hersholt and Bruce). Mayo and Hornblow, by the way, didn't smoke. The article goes on to say that compared to the others "...Bruce is the one who owns the largest number, all broken-in and fit for use. Nigel has bought and broken in an average of one pipe a week for the last ten years."
The article also states that "...during the filming of...Suspicion...Bruce offered to use his own pipes. The deal [with Hitchcock] was made at 50 cents a pipe. Bruce used as many as ten different pipes in as many non-continuity scenes. But he drove the script girl crazy. She had to watch that Bruce didn't enter a room with one pipe and then leave it with another."
For the die-hards I suggest watching Suspicion (always worth doing again) to see the ten pipes Bruce chose to bring from his collection to the set, out of the 500+ he's supposed to have had. For the less zealous, here's a photo taken on the set of Suspicion with Cary Grant and Nigel Bruce, the latter with pipe in hand (not a bulldog in this case):