Elementary...

"Through a great thundering mist, Alexander Jones heard THE WORDS.
"'Not at all. Elementary, my dear Watson!'"
- Poul Anderson and Gordon R Dickson, Earthman's Burden (New York, 1979), p. 121.

It had to happen.

People rightly say that Holmes never said that. But then why is it attributed to him? There are reasons why I think that it is a legitimate quotation. It would be more accurate if it were punctuated, "Elementary...my dear Watson!" but that is grammatically awkward.

(i) Holmes does say, "Elementary."

(ii) He does say, "My dear Watson."

(iii) Once, and I am not going to look it up now, he says both in quick succession in the course of a single conversation over two or three pages.

Therefore, it is legitimate:

to infer that Holmes would have said THE WORDS at some time in an off-stage conversation;

to attribute THE WORDS to him in some of the many sequels and adaptations.

In Casablanca: I think that the line "Play it again," is addressed to a character called Sam, hence that other spurious quotation, "Play it again, Sam."