Do I need to explain the example I gave? It's from The Blue Carbuncle:
The hat had candle-wax spattered on the right-hand side. When do you use a candle? When your house has no gas. When do you hold a candle over your head? When you're going upstairs. Why would you wear a hat on the stairs? Because you live upstairs. Why would you hold a candle in your right hand? Because your keys are in your left (dominant) hand.
None of the deductions are infallible. Deductions seldom are. In this case, none of the deductions are even important to the story. But there's nothing exaggerated about them either. It just goes to show that where it may seem like "psychic" powers are required, in fact it's just simple observation and deduction.
Yeah. Some of them are plausible.
It's the incredibly contrived ones that are hard to swallow. How many Londoners smoke cigars? Of those, how many import them from Blagistan? Of those, how many smoke a brand that can
only be gotten in Blagistan? And then that one guy is the guy that walks into Holmes' office?
Or, for every client that walked past a newly-constructed building with freshly-drying plaster imported from Crete AND also walked past the only chicken farm in the country where black chickens are exclusively bred, there are a hundred guys that walked past a newly-constructed building with freshly-drying plaster imported from Crete but walked past a
regular chicken farm. And for every one of
them there are a hundred guys that walked past a newly-constructed building with freshly-drying plaster imported from Crete but did NOT pass a chicken farm. And a hundred guys who walked past the building but
didn't get plaster on them at all.
So, a million people would have to cross his doorstep before one of them would have telltale signs on him that Holmes could pick up and make deductions.
A totally apocryphal example, but this kind of thing happens regularly in his stories. The stories are highly contrived to have signs to
be seen.