Zippy Monster, yes, ATC also have a reporting system that can alert the right people about potential callsign conflicts, it is how all the new alpha numeric callsigns came about in the first place. Many years ago in the days of Swissair, they sent 800, 820, 830, 840, 860 and 880 into the UK all at the same time. An hour later, they all departed but with a 1 on the end, exiting UK airspace through the same point. After a few confusions and a couple of safety issues, the whole callsign deconflicting really kicked off. Around the same era, BAW also sent 361, 551, 561, 631, 651 and 661 into the same bit of UK airspace as the Swissair's also entered at around the same time, not a happy Lydd Sector controller! There are some that are just bad timing (one late by a few hours and another a little early) and as I said earlier, still some that cannot be changed easily due to the international agreements obtained for those particular flights.
And then there was the day when Channex had two different aircraft in UK airspace using the SAME callsign.........