Society: Since there is no double-entry bookkeeping and little banking (as we would recognize it), there are unlikely to be large companies to own and operate telegraphs. Therefore the telegraphs, their manufacturing and all other capital-intensive organization seem likely to be owned and operated by the State/King (or a closely-related aristocrat), since only a tiny cadre will have enough wealth to build and maintain it.
The Crown's ownership of telegraphy, in turn, suggests fairly easy censorship and control over (rapid) information movement. The Crown can try use this to extend their dynasty and their wealth, with other aristocrats pushing back against the too-powerful King.
And then, as part of this political back-and-forth over a couple generations, some durned fool will teach the farmers and slaves to read, an incendiary will write a Manifesto arguing that the King Is A Fink and we don't really need him/her anyhow, and then the regimes begin to topple.
Warfare: With the ability to coordinate across distance reliably, look for bigger and more decisive battles, better intelligence, and a somewhat more responsive logistical tail. The actual size of each main body might be only slightly larger (or unchanged), but more units will show up on the battlefield on time.