In the first episode, the Spindrift departed from New York on its flight to London. In later episodes, the departing city is changed to Los Angeles.
Throughout the series, the Little People and the Giants would not have it so easy to communicate it to each other. The Little People's vocal cords, in relation to the amount of oxygen in their lungs, would not produce sound waves long enough for the giants to hear - even if they yelled. By the same token, the giants, with much larger vocal cords coupled with large volumes of oxygen from their lungs, would produce sound waves deafening to the Little People - even at a whisper.
In the first several episodes of the series, during daylight hours at the spaceship campsite, the sound of tropical birds can be heard. This was an obvious mistake on the part of the sound editor - on seeing the abundant foliage around the campsite, he probably assumed that the ship had crashed in a jungle setting (as per the series it was established as a giant city park). This sound track was removed in later first season episodes.
Right through the whole series, distances have proven to be quite malleable. Examples include: the little people can reach a destination at about the same time as the giants, despite their longer strides; the little people can cover vast distances (across the city etc) in a short time span; the little people can cover the same ground in a similar time as giants in cars.
In several episodes the women appear wearing different clothes. It is not explained where they get these.