• Visual similarity to Sidney Paget's illustrations
• The actor's ability to bring the personality of Holmes to life
• His Watson's accuracy
• The chemistry between the two leads
• The canonical accuracy of the screenplay
I have listed these criteria in what I consider to be their order of importance.
Visual similarity to Sidney Paget's illustrationsAs superficial as it may seem, a strong resemblance to the Paget illustrations is a must. Is it really coincidence that the best on screen performances have been given by actors who looked the part?
• Arthur Wontner
• Basil Rathbone
• Douglas Wilmer
• Ian Richardson
• Jeremy Brett
Wontner, Rathbone and Richardson - Three of the best.
• Matt Frewer• Ben Syder
• Richard Roxburgh
There have been good portrayals by actors that did not fit the Paget mould (such as Benedict Cumberbatch) but they are very much in the minority (and depend on the ability to meet all of the remaining criteria). It is also amusing how people who have never seen a Paget illustration seem to know when a Holmes looks right.
The actor's ability to bring the personality of Holmes to life
Sherlock Holmes has very definite character traits. His mood swings, his impatience with those less intelligent than himself and so on. However he has his softer, perhaps paternalistic, side and this needs to be shown. An extremely aggressive Holmes is as bad a mistake as a too emotional one. Christopher Plummer gave us an example of the latter in Murder by Decree.
His Watson's accuracy
Some people judge the quality of a Sherlock Holmes screen adaptation almost purely on the quality of the portrayal of Holmes but Watson is just as important. A bad Watson can drag a good Holmes down and a good Watson can go some way to rescuing a sub-standard Holmes.
Arthur Wontner, Basil Rathbone and Ian Richardson were all slightly dragged down by their Watsons. For Wontner, Ian Fleming was just too wet. For Rathbone, Nigel Bruce was too much of a buffoon and for Richardson, Donald Churchill was too pompous (and a buffoon).
Arthur Wontner and Ian Fleming (no not that Ian Fleming)
For the absolute zenith of accuracy we have to look no further than Jeremy Brett with his Watsons - David Burke and, later, Edward Hardwicke. These two men gave us portrayals of Watson that lacked accuracy in only one area. The area in question was age but the age of Holmes and Watson has been a constant issue since adaptations began.
The chemistry between the two leads
Good chemistry between Holmes and Watson is vital for a truly successful adaptation. Rathbone and Bruce had excellent chemistry and this went some way to offsetting the downsides of Bruce's Watson. Ian Richardson had an above-average Watson for his version of The Sign of Four and this went a long way towards making it one of the better adaptations. However, as a perfect example of how a bad Watson can drag an adaptation down, his Hound of the Baskervilles was much the poorer with Donald Churchill who lacked the all-important chemistry as well as being a poor Watson to boot.
Again Brett and Burke/Hardwicke demonstrate the best examples.
The canonical accuracy of the screenplay
Yes, as bizarre as it may seem, canonical accuracy comes bottom of the list. The most canonically perfect script will be ruined if the criteria above have not been well met. The recent Warner Brothers Sherlock Holmes demonstrated how a script littered with inaccuracies can actually work. Despite the script and the fact that Robert Downey Jr was hardly a clone of Paget's Holmes the film worked. This rested very much on the accuracy of Jude Law's Watson and the excellent chemistry between him and Downey Jr.
Another example is The Adventures of Sherlock Holmes with Rathbone and Bruce. The script was close to William Gillette's non-canonical stage play but succeeded largely because of Rathbone's excellent portrayal of Holmes (visually as well as in personality) and the excellent chemistry with Bruce. This formula held them in good stead through their largely non-canonical Universal films. This, I think, demonstrates, as well as it can be, how a canonical script, while desirable, is not mandatory if other criteria are met.