Taken just as you've written it, without examining the context, you'd need to center on "scrupulous meanness." Joyce says that he wrote Dubliners with scrupulous meanness.
Scrupulous means to have in mind what you believe to be right. It also means exactness and precision. So Joyce says that he wrote what he thought was right, precisely and exactly. He might also mean that he arrived at what he thought was right by exact and precise study.
Understanding what Joyce means becomes more difficult, though, when one adds meanness to the thought. He could mean one of two things, or both. First, he could mean that what he thought was right led him to meanness. Second, he could mean that he was not mean carelessly, that his being mean was the result of what he thought was right.
In short, the stories are the products of what Joyce thinks is moral or right. One might say that they demonstrate Joyce's "righteous indignation," without the usual religious, simplistic, and moralistic connotations those words might usually suggest.
In Dubliners, the shortcomings of Dublin residents, and the Irish as a whole and humans in general, are harshly exposed. Humans can be ignorant, superstitious, manipulative, psychologically impotent and paralyzed, etc. These weaknesses are exposed in the stories. One could conclude that the stories are written with "meanness."
Yet, the stories are not didactic--preachy or sermon-like. Joyce's narrators do not intrude (and neither does he as author) to condemn Dublin residents. Joyce does not appear to directly condemn anyone. Instead, weaknesses are revealed by narrative.
In short, Joyce exposes weaknesses, but, he says, he does it based on what he believes to be right, and he does it with exactness and precision. He is mean, but his meanness is based on what he carefully considers to be right.
In order to understand this, you have to examine the context and Joyce’s relationship with Dublin, which is an ambiguous one. Living in Dublin evoked sentiments of both love and hate. Joyce felt he was oppressed by the atmosphere of the city and was convinced that the artistic and spiritual freedom was to be found outside the confining walls of Dublin, which is why he eventually left it. Although he left it, Dublin was always the main focus of his works. In Dubliners, he wanted to show the state of spiritual paralysis which he felt the people of Dublin were overcome by.
The writing style of the collection is direct, unadorned, and realistic, and the speech is everyday, because Joyce wanted to present an accurate portrait of the city and its citizens, depicting the lives they were leading in the most authentic manner. The names of the places we see in the book as we read are as real as they can be, which allows us to connect with the book and the struggles of its characters. By presenting a realistic picture of Dublin and its people, Joyce’s hope was to let the people of Dublin know about their own spiritual crisis.
Joyce’s aim should be clear. He did not want to mollify the stifling effects which Dublin had on its residents:
I believe that in composing my chapter of moral history in exactly the way I have composed it I have taken the first step towards the spiritual liberation of my country.
Dubliners, he believed, were unable to change their lives because of the oppressive environment and its norms and were trapped in the monotonous routine which took away their potential for creativity, prosperity and fulfillment.