Toby, the dog from the Great Mouse Detective film (which has a slightly different name, for the UK market), is based off the keen-nosed dog from The Sign of Four of the same name--he is probably intended to be this dog, but he's of a different breed. Holmes has apparently also taken to keeping the dog close at hand--in ACD canon, he lives with a keeper.
The "German music, introspective and I want to introspect" stuff Holmes is saying to Watson when Basil and Dawson and Olivia pick up Toby marks the film as occurring at the same time, in ACD canon, as "The Adventure of the Red-Headed League" (RHL)--though the time of day is wrong for this utterance, and I'm not sure this was said in Baker Street vs in THE street. Also interesting: RHL is published in 1891 and set in October of 1890*. GMD is explicitly set in 1897--the year of actual!Queen Victoria's Diamond Jubilee, which, as in the film marked the 60th year of her reign.
What strikes me most about this parallel is how different the timing and the quality of relationships is. This takes place TEN YEARS
into Holmes and Watson's friendship, after Watson's married and, per Scandal in Bohemia, they've had quite a rupture in their friendship. It's published four years
into ACD's work on the canon, and two years before he tries to kill Holmes off by writing "Final Problem" (or one, in Canon Time). So what you have here is a Doylist/Watsonian gap of enormous proportions between the introduction of Basil and Dawson and that of Holmes and Watson, which might play out in Basil having quite different emotional relationships with his work and other people accordingly.
After all, Basil's material existence and his way of thinking about himself have not been affected by Dawson's presence as friend and biographer from his setting up in lodgings (essentially?) until this, his attainment of full adulthood. The AU!personality justification-spotting is possible, but seems something of a stretch--mostly what draws my eye is the sheer time-lag, the space it leaves in Basil's life for his vitriolic relationship with his nemesis to assume undue personal importance. It's perhaps important to remember that Holmes gives few to no personal fucks about his nemesis, and Basil is seemingly driven by and organized around this core--certainly the plot-action of the film is, and it relies on its protagonist to do this work.
Gentleman villain John Clay, while he doesn't really evoke Ratigan to me at all, shares his aristocratic pretensions--though little of R's deep anxiety regarding these. This is somewhat in contrast with Moriarty, who appears to give no such fucks. Clay is 'the third-cleverest man in London' at the time--presumably below the Holmeses? It's possible there's an element of paralleling Clay and R--the writers are fairly aware of the canon they're working with, down to that song in Ratigan's layer picking up the consistent ACD joke of Holmes obliquely referring to past exploits and flipping it, enforcing a degree of parallelism extra-textually.
Btw, this seems as good a time as any to point out the high-Dickensian bullshit humor of RHL. Why did I so strongly dislike this one as a child, circa 12 or 13? I trust my readings of Victorian lit from that period less and less now, I just don't think I knew how to deal with some of the period/stylistic shit. I also had some thoughts on the other one I listened to today, "A Case of Identity", but they're probably part of a larger post on Holmes: Non-Sociopath and maybe also on Watson as unreliable narrator (predicated on "Scandal in Bohemia").
* "The dates given in the story do not match the characters' descriptions of time passing. The date that Wilson sees the advertisement is April 27, 1890 and he has been at work for 8 weeks and says "Just two months ago." Thus that happened by the end of June. However, the date on the door telling of the League being dissolved is that of October 9, 1890, six months after the ad was placed. The two previous dates are consistent and thus this October date is incorrect, if it has any meaning.
Dorothy L. Sayers analyzed this discrepancy and claims that the dates must have been August 4 and October 4 respectively."--per Wiki