What are the themes of the Victorian age we see in The Warden?

The Warden, published in 1855 at the height of the Victorian age, reflects the Victorian theme of exploring social injustice, which was popularized by Dickens as well as contemporary novelists from other countries, such as Harriet Beecher Stowe in Uncle Tom's Cabin. In Trollope's novel, John Bold challenges the income disparity between the warden, the gentle Reverend Harding, and the twelve elderly inmates, called bedesmen, of Hiram hospital, a religious establishment that Harding runs. This novel, albeit in a mild way, explores the growing concern of the times about the income disparities between the rich and the poor. Social privilege and the poverty it causes is coming to be seen less as inevitable act of God and more as a social problem that can be engineered away. Trollope shows the newspapers attacking the gentle Harding as greedy.
Typical of the mainstream Victorians, however, Trollope's concept of reform is not political as much as personal. The story hinges not on reforming the clergy in the Church of England in a systemic way, say through legislative reforms, but on the benevolent and moral stance of Mr. Harding, who, when he realizes the injustice, refuses to stay in a position that he believes pays too much at the expense of the inmates. The bishop decides the warden position will remain vacant once Harding resigns but does not give the money to the bedesmen. The novel shows that doing the right thing carries its own reward, as Mr. Harding lives comfortably in his new—if greatly reduced—circumstances, and his daughter is able to marry without a dowry.

Trollope's The Warden reflects three major developments in Victorian culture and ideology. 
The first issue Trollope raises is the role of newspapers and investigative journalism. In his picture of The Jupiter (a stand in for the Times) he tries to show how the media, in their quest for stories that sell and scandalous headlines, can often mislead or harm people.
The next issue that Trollope engages is the shifting religious landscape. He shows the Church of England moving from the gentle benevolence of the Reverend Harding to the more dogmatic positions of the strict high churchmen and evangelicals. Harding is the most sympathetic character of the work and through him Trollope argues for the need for human kindness and community rather than dogma.
The third issue Trollope addresses is the shift from personal benevolence to a rule of law in charity. In one sense, Trollope shows us the positive side to ending corruption and establishing a rule of law, but on the other hand, after all the scandal and disruption, the residents end up worse off than before.