I've already learned that Wizards are unique in that they can learn new spells by finding them. Can they also learn a spell by watching someone else cast it? Can any other class do this? Or at least know what's being cast?
Wizards learn new spells from scribing them in their spellbook. Simply seeing a spell being cast is not enough information for a wizard to copy the spell in his spellbook. However, he can copy a scroll in his spellbook, which renders the scroll useless.
Other classes all either have a spellbook, which means the above applies, or a set amount of spells known (be it limited or not*), which means they can only learn new spells by leveling.
Every class can make a Knowledge Arcana check to see if they can recognise anything related to magic, be it magical creatures or spells, and see if they remember something about them. For the creature, these could include strengths and weaknesses, but could also include if they are usually in groups or what the creature eats. For the spells, you can recognise the spell and its properties.
*Some classes know all the spells in their spell-list immediatly, hence a set amount, yet unlimited, in a way.
While it's not mechanically possible, "Hey do you remember that one Goblin that cast that ball of fire? I've been copying his moves, check this out" sounds exactly like how a Sorceror picks his new spells when he gains a level.
So flavorwise, it's definitely in line with the Sorceror and his intuitive grasp of how to perform magic.
Wizards study, so it is very weird for them to learn something just because they saw it happen once, but Sorcerors just make it up as they go.