The school in the movie is William Dawes Elementary. William Dawes was one of the riders who, like Paul Revere, warned the minutemen that British troops were coming. Just like a child at his namesake school was trying to warn people what was coming.
The piece of classical music we hear at the start and again at the very end of the film is Ludwig van Beethoven's "7th Symphony Major, 2nd Movement - Allegretto in A Minor". Completed in 1812 and dedicated to his friend Count Moritz von Fries, the work premiered in Vienna at a charity concert for soldiers wounded in the Battle of Hanau and was encored.
The text of the time capsule plaque reads, "We, the 3rd grade class of William Dawes Elementary School, in the year of 1959 A.D., hereby commit our visions of the future as a token of hope and friendship toward our successors, the class of 2009 A.D."
When John Koestler is teaching his class at MIT at the beginning of the movie, the equations behind him on the blackboard are James C. Maxwell's equations of electro-magnetics. The Earth's magnetosphere is what protects us from harmful solar radiation called "solar wind" by channeling these particles to the Earth's magnetic poles, causing the phenomenon known as the Aurora or Northern Lights. This same solar wind, when extreme, cannot be fully mitigated by the Earth's magnetic field and may cause electrical and radio communications problems. Theoretically, a very powerful solar emission, such as the one which destroys the Earth in the movie, is a very extreme case of solar wind, called a Coronal Mass Ejection. Hence, the equations on the blackboard are a subtle and clever hint of what will happen later in the movie. Additionally, the equations are, rather unusually, given in spherical coordinates, with rudimentary drawings of a circle (possibly representing the Sun) and the Earth and its magnetosphere, all of which indicate that this is a deliberate and clever hint of the movie-makers. However, NASA has recently predicted that a very big solar wind would hit the Earth on the proposed "End of the Year" year of 2012, but it may cause communication problems.
After realizing that the cataclysm will come in the form of a coronal mass ejection (CME), John Koestler states that the effects would be on the order of 100 microtesla. Geomagnetic storms are measured by magnetic disruptions at the Earth's equator, expressed in nanotesla. A strong storm would be 100 to 200 nanotesla. Therefore, a 100 microtesla event would be 1,000 times stronger than this and certainly cause the disruptions to electronic devices as portrayed in the film.
At the end of the film, Caleb and Abby are seen running through a golden field toward a glowing tree, after being dropped off by the beings. The two kids could represent Adam and Eve in the Garden of Eden with the Tree of Life. Also, the beings also resemble what angels are perceived to look like when they reveal their true form.