How did Holmes deduce that Watson had a careless servant?

A Scandal in Bohemia is Sir Arthur Conan Doyle's third Sherlock Holmes story, which was first published in The Strand Magazine in July 1891. Conan Doyle wrote sixty-two Sherlock Holmes stories between 1887 and 1927, including fifty-eight short stories and four novels.
Conan Doyle became disenchanted with the Sherlock Holmes stories and thought they were eclipsing his other writings, so he killed off Sherlock Holmes in the twenty-sixth story, The Adventure of the Final Problem, in 1893.
There was a public outcry, and that uproar, along with the urging of his family and his editor, caused Conan Doyle to reconsider Holmes's demise. He resurrected Holmes in 1901 and wrote thirty-four more Sherlock Holmes stories in the next twenty-six years.
Even in this early story, Conan Doyle has Sherlock Holmes demonstrate the same clear, straightforward, and incomprehensibly simple method of deduction that he exhibits throughout all sixty-two stories.
In chapter 1 of A Scandal in Bohemia, Holmes somewhat uncharacteristically engages Watson in small talk about domestic matters.

“Wedlock suits you,” he remarked. “I think, Watson, that you have put on seven and a half pounds since I saw you.”
“Seven!” I answered.
“Indeed, I should have thought a little more . . ."

Holmes then observes that Watson has been getting himself "very wet lately" and that Watson has "a most clumsy and careless servant girl."
Watson is taken aback, as usual, by Holmes's remarks and asks him how he came to those conclusions.

“My dear Holmes,” said I, “this is too much. You would certainly have been burned, had you lived a few centuries ago. It is true that I had a country walk on Thursday and came home in a dreadful mess, but as I have changed my clothes I can’t imagine how you deduce it. As to Mary Jane, she is incorrigible, and my wife has given her notice, but there, again, I fail to see how you work it out.”

Holmes takes the opportunity, as usual, to show off his remarkable skills of observation and deduction. This time, though, there is no lengthy explanation of how he arrived at his "double deduction," as sometimes occurs in other stories.

“It is simplicity itself,” said he; “my eyes tell me that on the inside of your left shoe, just where the firelight strikes it, the leather is scored by six almost parallel cuts. Obviously they have been caused by someone who has very carelessly scraped round the edges of the sole in order to remove crusted mud from it. Hence, you see, my double deduction that you had been out in vile weather, and that you had a particularly malignant boot-slitting specimen of the London slavey." [A "slavey" was a maid who performed the most menial duties in a Victorian household.]

Once again, Watson is amazed and astounded at the simplicity of Holmes's reasoning, and equally amazed and astounded that he couldn't do it himself.

“When I hear you give your reasons,” I remarked, “the thing always appears to me to be so ridiculously simple that I could easily do it myself . . . I believe that my eyes are as good as yours.”
“Quite so,” he answered, lighting a cigarette, and throwing himself down into an armchair.
“You see, but you do not observe."

Due to the nature of Holmes's deductive abilities, and the incredulity of those around him who witness him solve the crimes, variations of this same conversation appear in all of the Sherlock Holmes stories.