It's not actually about the daily complexities of weather, but rather about the long term trend towards higher average temperatures across the latitudes over long periods of time. Science has been getting very good at doing that lately, and the recent detailed analysis of the ice-core samples from Antarcrica enabled the IPCC to come to the conclusions that they did with high levels of certainty. Nothing is ever totally certain when you predict into the future, but the scientific consensus on this is unusually high, despite what some of the media might like us to think.
Incidentally, although Al Gore may not spell out the background science in the film, he does have penty to back up his claims in the presentations he gives, and he is supported by an increasing number of organisations across the world in this regard. In the UK, the University of Cambridge Programme for Business and Industry recently invited around 100 people from across the country, including some from education, the media, local and national government, NGOs and a variety of businesses and industries to a 2-day seminar session with Al Gore. He was challenged on a number of counts by some of the delegates, but was strongly supported by all of the scientists, including the current director of the British Antarctic Survey. For a politician, he has a surprisingly good grasp of the science, and he responded very well to the challenges.