Yeah, the non-starts can be annoying. The spiel approaching the TTC on the Epcot beam (the one that talks about the various transportation options from the TTC ) usually fails to go off unless you hit the sensor at a reduced speed (something like 20-25 MPH, I think). This doesn't usually happen, though, as the speed limit in that area is 30 MPH and, even if there is a train ahead at the TTC, the pilot wouldn't start slowing down until after that curve (the one where the tracks on the Epcot beam split and the one towards the TTC turns left). Another common offender is the first spiel as the train enters Epcot, though it is not as bad as the TTC one and there doesn't seem to be a way to better the chances of it going off. In some cases, though, such as the area from shortly after leaving the MK to the Wedding Pavilion on Express, the spiel has simply been removed. Likewise, the one on Express when going through the Contemporary has been thinned down a lot, too.
Sometimes, the cut-offs were actually caused because the spiel was too long to play in the space allotted. There was one particularly long one coming back from Epcot that started right after leaving the station and continued all the way to the first billboard on World Drive and used to go on and on and on about the parks, Disney Vacation Club, and who knows what else (since we almost never heard the whole thing). In some cases, pilots would even try to make it to the next spiel trigger as quickly as possible (within the safety restrictions, of course) in order to cut off some of the spiels. (That long one and several of the other DVC ones were favorite targets for intentional cut-offs.) Also, the PSAs and the regular spiels cut each other off. If the final boarding call spiel is played, it will cut off the spiel that plays when the train is in the station. Likewise, if the MAPO test spiel is played out on the beam and the train goes over the next spiel trigger, it will cut the MAPO test spiel. (That is why I tended to wait until the MAPO test spiel was over before I moved in areas where I knew that would happen or I would play the holding spiel as soon as I knew that I would probably have to stop, in order to keep the regular spiel from interrupting it as I approached the holdpoint.)