In this story, we see Holmes do something which he seldom does: lose his cool. In their initial meeting, Milverton comes off better than Holmes, who is frustrated enough to consider physically accosting the man and taking the incriminating letters by force. Had he been thinking as clearly as usual, Holmes would have known that the master blackmailer would never risk his leverage that way. Also, the normally eagle-eyed Holmes would have realized that Milverton was carrying a revolver under his coat. But Holmes seems to have a personal loathing for Milverton which surpasses his distaste for other criminals with whom he's dealt.
It's interesting to note that frequently it is these cases of maliciousness and greed resulting in the deliberate ruination of lives which raise Holmes' ire, more so than a straightforward theft or murder, which he approaches more clinically. For example, in A Case of Identity, when Holmes discovers the hoax being perpetrated by Mary Sutherland's stepfather to keep her from marrying and retain the use of her inheritance, he is angry enough to threaten to horsewhip the scoundrel. Yet before we get too far in proclaiming Holmes' nobility of purpose and character, let's remember to what lengths he is prepared to go to, to break this case. In his disguise of a plumber, he courts and proposes (!!) to Milverton's housemaid in order to gain access to the house and information about Milverton's comings and goings. When a scandalized Watson remonstrates with him, Holmes airily waves away his concerns, saying that there is a jealous suitor waiting in the wings to take his place when he-in plumber guise- disappears. Of course, it can be argued that an engagement formed after only a few days of courting is obviously a shallow connection, but still... it's a cold thing to do.
Once again, we see the strength of the friendship between Holmes and Watson demonstrated in this case. Despite his misgivings about the wisdom of Holmes' plan, Watson makes it clear that he's all in, even when Holmes humorously points out that they may both wind up in a jail cell if things go wrong. Indeed, he stubbornly threatens to tell the police himself if Holmes doesn't let him participate in the burglary. Meanwhile Holmes, out of his concern for Watson, originally refuses to take him along, preferring his friend not put his reputation and medical practice at risk. In the end though, he acquiesces to Watson's demands and takes along his (this time, literal) partner in crime.
In Part II of my examination of The Adventure Of Charles Augustus Milverton, I'll discuss what actually happens when the two men break into Milverton's house, the origins of Mr. Milverton, and the differences between morality and legality.