In Diablo 2, certain bosses, such as Andariel had a weakness to fire. Do any of the bosses in Diablo 3 have any specific weaknesses that I can exploit on higher difficulties?
Some notes on boss fights in the earlier difficulties, this does not address Hell and esp. Inferno with the enrage timers.
General strategy for team play
If there are weaknesses, they are not in the way for example pokemon works (beating fire with water). The elemental damage in D3 is different from the D2 elements. In a way elements have become a purely visual gimmick. Resistances are still important for your own equipment to survive certain champions but you can kill them either way. Information about the Boss HP is aviable but not about resistances afaik. If you want to exploit the bosses on the higher difficulties you should do it in the way of survivability vs dmg output vs movability. But you don't have to think about killing diablo with Ice spells instead of arcane.
Most bosses in hell and upwards can be exploited the same way they were in the lower difficulties: by evading their attacks efficiently to reduce their dmg output. Try to heal yourself up rather sooner than later so you don't get suprised when a sudden burst kills you.