To the best of my knowledge the 'Blue Pullman' units were the first to have PA systems in the UK. I have yet to find any detailed information but I would hazard a guess that the system was based on aviation technology (I believe PA systems were established in passenger aircraft by this time) and used valves.
The 1966 Manchester Pullman stock was also PA fitted as built, but I don't know if this used the Ripper system or was a bespoke installation.
Mark 2d and subsequent loco-hauled stock were fitted with Ripper Robots equipment, which transmitted along the existing carriage lighting control wires and therefore required no additional cabling between coaches. As mentioned above, many earlier vehicles were retrofitted with this kit. Some years back I found the schematics on the Web (it may have been a link from this very forum) - I had always thought that it was a carrier wave system but it's actually nothing more than a balanced audio signal transmitted down the train.
As for multiple units, I'm not sure which was the first. Class 313? Like hauled stock, much was retrofitted. In the case of the Southern slammers the PA used the same wires as, or was closely related to, the guard-to-driver communication. I can certainly remember it going 'click click' when the guard signalled the driver to depart.
Any problems with valve technology in the early days would have been a result of the vibration prevalent in a train-borne environment. Otherwise, it was very reliable, certainly after WW2. Static equipment, such as station PA amplification, was installed, switched on, set up and then left alone for 20 years or more, much the same as today. The problem with valve amplifiers on transport was that they were big, heavy, gave off lots of heat and required complex power supplies. Transistor equipment, on the other hand, can run directly from the 24V DC carriage lighting supply.