This entire process represents three feats by Holmes:
1. Watson gained weight
2. Watson returned to the medical profession
3. Watson has a servant who is terrible at her job.
Holmes fires this information off rapidly, receiving confirmations from Watson, and replies that "'It is simplicity itself.'" He then goes into detailing his reasoning, siting information such as the amount of cuts on leather and a bulge on the right side of Watson's top hat. None of these facts are given to the reader at any point, and so there is no way for the reader to follow along with these explanations beyond putting faith in Holmes. The text, in fact, makes it impossible to read without trusting him and his prowress.
Additionally, these observations that are mentioned are ones that it is unlikely many would notice; or, at least, no one would notice all of these facts at once and come to such a breezy, rapid-fire set of conclusions. This depicts Holmes as being beyond intelligent, and further establishes his credibility to the reader as well as the awe that the audience is supposed to hold for him.