I was travelling from Carlisle to Newcastle a few years ago on one of the through services from Scotland, a ScotRail 156 but crewed by Northern. The automatic station announcement immediately got out of sync, and, after departing from Haydon Bridge, a passenger sat opposite me checked with the guard when he passed that the next stop was indeed Hexham.
The guard confirmed that it was, apologised for the confusing PA, and blamed it on the fact we were travelling on a Scottish train and the time difference between England and Scotland (and then went of to reset the system). After the guard had gone, the passenger looked at me and asked, "Is there a time difference between England and Scotland?"
A few stops further on, the gentle Scottish automatic announcement said we'd soon be arriving at "Prood-hoe" (locals pronounce Prudhoe to rhyme with udder).
Further south, guards on Anglia Railways (remember them?) always announced the end station as "where this train completes its journey" instead of using the more common "terminates". I've heard it more recently on Greater Anglia rural services as well (although don't travel by train as much in the UK as I used to).
And then there was the evening we were approaching Cambridge from the north, when the guard added a warning to watch out as the train crossed over the points (implying some sort of swerving as we entered the bays at the north end of the station). Having seen which route was set, he then announced the platform and which side the doors would open, finishing with, "I hope you had a good sleep, madam."
Regarding announcements at stations, the Train Announcer (official BR term - not station announcer: they announce the trains) at Oxford was, unusually, located in the TEB (Telephone Enquiry Bureau) rather than the power box, and as a student I once worked there for a couple of months. A problem of this arrangement was that the announcer couldn't see the panel and the location of trains. One afternoon, during the usual quiet spell in the TEB, a train was announced with its usual platform, but the platform had been changed and the signalman immediately phoned to inform the announcer of this fact: so he had to make a correction. He began, "This is a correction to my next announcement" and then had to stop because everyone else in the office suddenly cracked up laughing.
On another occasion, the day's relief announcer, who was also a volunteer guard at the Great Central Railway, announced, "The train at platform 1 is the ten hundred hours Network Express for Rothley, correction Reading, and London Paddington." All accidentally, of course!