The bird calling as they approach the cottage in the Triumph Stag is a European golden plover - not an appropriate species for the geography, habitat or time of year.
The killer somehow got a CAR into a swimming pool that appeared to be accessible only on foot and by a narrow covered pathway. Nonsense.
The dead teacher's sister finds herself accidentally playing to the teacher's class of 7-year-olds a tape which turns out to be their teacher in a distressed state talking about her own forthcoming murder. Any adult finding themselves in that position would stop the tape within seconds to avoid traumatizing the kids - but instead the sister just keeps it running.
Someone else has said it would be impossible to get a car into the pool. But it is only a Mini and it's far from clear what the actual layout of the property is. Near the end a concrete mixer lorry seems able to access the pool. If that can be done then a Mini should be no problem.