The genesis of Holmes' detecting - 'The Adventure of the Gloria Scott' - [GLOR] is a good place to start when discussing the problems of Sherlockian chronology.
The story itself is actually a story-within-a-story. Holmes is relating the tale to Watson "one winter's night on either side of the fire." There is no way to tell when they are sitting around that fire, and it isn't necessary to know. (A few have tried, though, and come up with some decent arguments with very little evidence.) The part we're interested in is the part that concerns the ship the Gloria Scott, Holmes' old friend Victor Trevor, and Victor's father.
What we know of what Holmes calls "the first case in which I was ever engaged" is that it all started "during the first month of a very long vacation." Later in the same paragraph we find that it is autumn. We also know that Holmes is in college, and that he has been conducting some experiments in organic chemistry. If you read more you find other little references that would seemingly help date the thing, but in the end you discover that none of them make any difference until you solve the biggest problem in the case. What is that? Well...
When the senior Trevor sees Hudson (an old shipmate) for the first time in a long time, Hudson says, "it's thirty year or more since I saw you last." Why is that a problem? Later in the narrative we find that Hudson and Trevor had committed mutiny in the year 1855 when the Crimean War was in full swing. If you take the 30 years (or more) Hudson refers to and add it to 1855 you get 1885 at minimum. That causes a lot of problems in the Sherlockian Canon. How? If this story takes place while Holmes is in college then we should be talking about the mid-to-late-1870's. If we accept 1885 as correct then it means Holmes could not have met Watson in A Study In Scarlet [STUD] in 1881 (or 1882, 1883, or 1884 as some chronologists believe) and that Holmes must be about 10 years younger than what we thought. It also means that every single story that has been dated to between 1881 and 1885 must be wrong.
Okay, you say, what if it's just a mistake and he meant 20? There is evidence of that. Trevor later says that "for more than twenty years we have led peaceful and useful lives." That 'number' when added to 1855 would certainly work a lot better. The argument here is that Mr. Trevor didn't correct Hudson when he said 30. But, there is more evidence for the 30. Senior Trevor himself says during his explanation of what happened that "the laws were more harshly administered thirty years ago than now." So, which number do you believe? Since both men talk about it it's not as easy to dismiss. If only one had I might lean toward believing that 30 is just an error that happened somewhere in handwriting or typesetting. (I hate using those excuses.) However, the 30 makes no sense. One would have to accept a number somewhere around 25 for it to work perfectly.
I never actually settled upon a date for this story, but everyone else has. Each had to basically ignore the 30 to get their date, but still the years range from 1873 to 1880 depending on which chronologist you're reading. Most place the year in the mid-to-late 1870's.
The reason no one can accept "thirty year or more" is (besides the reasons I gave above) that nearly every chronologist agrees with Watson when it comes to his date for 'The Adventure of the Speckled Band' [SPEC] as April of 1883. If that year is right then the events of GLOR (Holmes' first case) could not have happened in 1885. Also, 'The Adventure of the Musgrave Ritual' [MUSG](another early case - 1878-1881 or so and pre-Watson) makes mention of STUD and GLOR in its text. That means those three stories all predated SPEC, and that means that GLOR had to have happened before 1883.
So, do you see how difficult it can be? This is Holmes' first case ever, and right away we have a problem. Luckily we don't have the same problem when it comes to dating his last case, but there is a lot of debate for the other 58.
We'll start tackling those next time.