The citizens doubted Sita because she had stayed in another man's home for so long. They could not understand how any woman could have withstood so long. They could not imagine that anyone could be strong and hence the doubts. For them it was impossible and so they judged even Sita according to their (the common people's) standards. If they had been educated and intelligent enough, they would have appreciated the strength of character she had shown. Ram was much above the ordinary man - he was a king. A king must understand the mentality of the common people and act accordingly. Hence, punishing the citizens, would have been like punishing someone who had committed a crime (though completely heinous) unknowingly. Besides, if they had all fallen at his feet and asked him to spare their lives, Ram would have had no other choice - he would have spared them.
As to why Ram threatened Mother Earth - she was the one who took his Sita away. Threatening her could have made the Earth give Sita back - so that she, as a Mother to all who live on the Earth, would give back Sita to save the other lives. Killing the people of Ayodhya would definitely not bring back Sita. At that moment, (my guess again) I think all Ram knew was that his Sita is being taken away by the Earth and he wanted her back at any cost and nothing else mattered for him.
Deepa - excellent comments.
The one thing which I did not understand in the episodes was that when Sita said that she was leaving the Earth everyone bowed down to her - it felt as though everyone were saying goodbye. Is it just me or did I miss something important and misunderstood the whole thing?