Throughout all three seasons of Father Ted, and more importantly this episode, when we see the outside of the Parochial House we can see no trees nearby. However, in this episode a tree falls through the roof.
In "Think Fast, Father Ted" they get the car. However, they have the car in previous episodes such as "Hell".
Ted says that the Nigerian villagers who left on a boat to avoid the boring priest were eaten by alligators, but there are no alligators in Africa.
Dougal says that the car seems to be 'not too bad', but when Ted has a look at it, the front end is intact but the rear end is crushed. However, Jack said that the car had hit by two trucks. Assuming the trucks hit from the same direction, it is more likely there would be damage to the front of the car as well. At worst, the car would be completely crushed, leaving them unable to drive it.