Gore's speech was notable for being funny; the first few minutes were mostly jokes about the 2000 election -- how Gore went to sleep counting and recounting sheep, or how he was the first person laid off under George W. Bush. The stress in his speech was internationalism and environmentalism, and he lauded Kerry's environmental record. Carter had the role of elder statesman, and while his voice was a little slurred at times, he gave an evocative talk about human rights and how the White House squandered the goodwill it had after the 9/11 attacks. HRC's speech was strident, with a focus on the health care crisis and about leadership, and it led into Bill Clinton's long and amusing oration. The former president used the device of showing the difference between the parties again and again, showing the Democratic policies in a good light, while pointing out the flaws in the Republican view. I really liked his point about the unfairness of the tax breaks under Bush; when he said that he considered sending Bush and the congress a thank you note about the cuts for the top 1% but then realized that those cuts were financed by raiding the social security surplus and borrowing money from abroad, I was hooting and hollering down on my futon.
Salon's got a good article on the first night at http://www.salon.com/news/feature/2004/07/27/clinton/index.html. Their writers do a better job than me at analyzing the role of the speeches. However, in my role as a partisan fan, they did a great job in getting me more excited about the race, and I'm eager to see what else will come up by the end of the week.