Pretty bad tensions emerging fairly soon, I guess. There are a few unaddressed problems that will break out in the course of the next few decades:
- Italian nationalists will perceive this as a huge slight. Rome is the capital of Italy, as far as they are concerned this is not a negotiable position. You could see a deep and lasting divide between the Church and large parts of the Italian right and moderate patriotic vote. Perhaps a more clearly developed tripolar political system - Right-wing nationalists, left-wing Socialists and the religious conservatives? Zentrum with a vengeance. Given the international guarantees, I don't think it would necessarily lead to war, and eventually the government in Turin (Florence? Milan?) would acept realitioes much like the Netherlands reconciled themselves to the existence of Belgium.
- The liberty gap will continue to exist. The papal states were not like the Vatican City, no kindly spiritual retreat where a bunch of elderly sages pondered moral philosophy while picturesque Swiss guards and contented wokers met their every needs. They had a real military, a genuinely nasty secret police, and a large (and to a large part unhappy) population of laypeople. Rome was still a large-ish city, with all that entailed, international traffic, news flow, a press, politics, a working class. And the Papal States were not run on theology or Catholic Social Teaching, they largely ran on undiluted tradition. This was a government that would hae its police take away the children of Jewish families secretly baptised by their Catholic nannies. IIRC they hadn't executed a heretic in quite a while, but the laws were on the books. You could certainly do time for thoughtcrime. Once some parts of the Papal states become part of Italy - with its zest for industrial development, relative political freedom and embracing of modern technology - you get a visible divide. I wouldn't take the East Germany/West Germany analogy too far, but I could see Lazio getting problems with both productive labourers leaving and political agitators coming in.
- That takes me to three, the incredibly toxic nature of this state for the standing of the Catholic Church in many nation-states. stories of life in the papal enclave will leak out and no doubt be embellished, and now every Catholic priest is as representative of a regime mentally filed with Tsarist Russia and the Ottomans. Pius IX may well do to political Catholicism what Stalin did to Communism. He was a divisive enough figure OTL.
I don't see an easy way out of these traps for the papacy, either. The entire logic of the system is geared towards intransigewnce. Bowing to superior power and accommodating to whatever the secular state mandated (while loudly protesting its abuise and captivity) was a possibility because it was the only viable choice. I don't see how any pope can gracefully accede to reforming his state and doing what those secularists tell him to. It will take enormous pressure and long time - time that, with discontent inside the borders and anticlericalism rife outside, may simply not be there ITTL.