I really like this idea, I've actually sort of toyed with it before (a sort of post apocalyptic Victorian-era, but really just a major population drop and a regression to a few centuries before). This made me remember that scenario and kind of rework it... Here are the results, tell me what you think, I'm sure it's horrid... This is more meant to be dramatic AH than totally plausible AH.
Civil War; France and UK realize USA is getting too powerful, intervene on the side of the South. During the war, biological warfare is used for the first time; a french scientist develops a method for deployment of [horrible disease] in several northern cities. The north is forced to sue for peace as the government is basically collapsing, with people fleeing the core cities to avoid the plague.
The border between the USA and the CSA begins to resemble OTL's border between North and South Korea. Huge fortresses with complicated trenchworks arise on both sides. Washington DC is essentially turned into a big military base. The rest of the border is heavily patrolled by southern cavalry, to prevent refugees from the north from bringing in more plagues. No one is allowed across. Both sides spy on each other constantly, and there are guerillas in many places on both sides of the border still fighting the war unofficially. If you want to go in between you have to around through either Mormon territory, or through California/Cascadia/Canada. The north is pretty dystopic, because the government is really poor and its had basically this major holocaust. Huge numbers of people die (here is where I would put some actual population statistics if I was good at AH), and the little money that the government has all goes into maintaining the military. The government becomes increasingly authoritarian/fascist in an effort to harness the labor-power of recent immigrants to maintain what little industry is left. Needless to say, ITTL immigration from Europe dries up fairly quickly, though there may still be limited amounts to the CSA and the independent western states. There are lots of intelligence officers on every street corner, and the government seems everywhere. The feeling is sort of post-apocalyptic, with the largest cities like New york and Boston being somewhat barren, with so many people having died or run away. Occasionally plagues will break out again from time to time...
This is one reason the CSA is so keen to protect their side of the border; a few times their military plagues have come back and bit them in the ass, so now they also spend an inordinate amount of money (much of it borrowed from the UK, France, and Brazil [I have vague plans for Brazil to be a big deal in this timeline, as it receives many more of the immigrants who went to America IOTL) maintaining their military presence along the entire border. Needless to say the government is very oppressive here as well; violence is a part of everyday life in the south, with duels, riots, and slave revolts common occurrences.
Meanwhile, in Europe, all kinds of people are horrified by the atrocities the governments have committed. People start dealing with it by both legal and extralegal means, so many of the officials responsible are tried in court; but some of the higher-ups are able to escape by claiming they weren’t involved; since they don’t take responsibility the courts let them go, but individual vigilantes begin to take them out. basically over a short period of time assassinations, anti-government terrorist bombings, and duels become very common in the capital cities of the UK and France, and personal freedoms are curtailed as a result. By the 1870s it becomes much harder for ordinary citizens to freely travel around the western world in general -- even within their own countries. Cities that have not begun their police departments yet do so, and cities with police arm them more and more.
Tensions flare with regards to Germany; France knows of Prussia’s ambitions and cannot allow them to happen, and so consistently tries to undermine their attempts at dominating Germany. Something like the Franco-Prussian war breaks out in a similar timescale but France is a bit more prepared for it. They have more gatling guns and deploy them with their infantry instead of with their artillery, along with other doctrinal and technical changes and a bit of luck. The war goes on for longer (a few months) before the French army routs. However, since the war was much more taxing on Prussia it is not as able to unite germany.
The ultimate results by the 1880’s-1890’s.
-Britain: Still the most powerful country in the world, but with an extremely bloody past. Using chemical and biological warfare in crimea and during their intervention in the *American Civil War and *Franco-Prussian War (and possibly the *Crimean War?? Or does that take the POD back too far?). Extremely brutal colonialists in India, Australia and Africa as OTL... at home, almost no democracy. Victoria has dissolved parliament and granted control to a military junta who care little for human rights. All dissenters are repressed under a General who some quietly term the "New Cromwell."
-France: the *Franco-Prussian war lasted longer than OTL but was ultimately more destructive. the central government has completely collapsed. Some liberal revolutionaries attempted to establish a republic, which was recognized by the UK. On the other hand, some parts of the country are dominated by socialists, who argue between reformist vs revolutionary tendencies. One of the characters in the story can be Marx himself!
-USA: All the land west of the Dakotas and south of Oklahoma has been lost. Population centers have been drained due to plagues, and are mostly abandoned. The government struggles to maintain control over a fractured society that is more-or-less abandoning industrialism in favor of rural subsistence farming, far away from urban centers. What little industry remains is jealously guarded by the military, who use it to maintain their impressive fortresses along the border with the CSA, and to a lesser extent Canada and the new western border. A few hyper-rich industrialists remain, amongst the now-empty highrises of NYC or in the fortress-city of DC.
-CSA: Riots, slave revolts, and terrorist attacks are common in the south. The government is barely around, and has mostly privatized the military into several mercenary companies. British pounds pay their salary in return for an uninterrupted source of cotton for british textiles.
I need to work on the rest of the world, of course, these are just the countries that are most obviously relevant... I was thinking that as a result of Germany not uniting, science would be held back somewhat. I know how much German scientists contributed to all of our knowledge in this period; though obviously this wouldn't be stopped ITTL it might be a less focused and sustained trend, nor might it receive the same funding...
Could the Difference Engine be used for evil?
I think only in a sort of indirect way, like how the Nazis used early IBM computing machines to keep track of records of who they were killing in the death camps or whatever. An evil country could gain some advantages from having a functioning Difference Engine, and more still from a functioning Analytical Engine.
EDIT: Another thing I was thinking. Especially in the late Victorian period, Eugenics was very much in vogue.