You might like to analyse the humour in this short excerpt. There is a sense in which, as in all of his fiction, Twain uses hyperbole or deliberate exaggeration to great effect. Perhaps the most obvious--and hilarious--example of this comes at the end of the essay as, despairing of every getting his watch properly fixed, the narrator takes it to a watchmaker whom he identifies as being a former steamboat, who was "not a good engineer, either." His advice, that treats the watch as if it were a malfunctioning steam boat, is hilarious, but note how the narrator responds to this:
I brained him on the spot, and had him buried at my own expense.
Of course, the speaker would not have committed murder, but this throwaway line helps to convey his frustration and anger at the ineptness of the engineer and how he is unable to get the watch fixed.
Secondly, you might like to consider how the watch is personified to emphasise the way in which something is wrong with it. Note how, after the first "repair," the watch is described as being a sick human:
Within the week it sickened to a raging fever, and its pulse went up to a hundred and fifty in the shade.
This personification gives the watch its own distinct character and also helps to convey the way in which it sped up so greatly.