|Cerveza - good for practising your pronunciation|
The biggest grammatical difference is that in Spain 'vosotros' is used for the second person familiar plural, whereas in Latin America 'ustedes' is used.
The biggest difference in pronunciation I think is the Castillian lisp, widespread in Spain but not seen in Latin America. This means that the soft 'c' and the 'z' in Spain are pronounced with a hard 'th' sound, like the 'th' in thought. In Latin America these letters are pronounced exactly like the 's' which is always a hard 's' sound like the 'c' in voice.
So cerveza (beer) is pronounced ther-vay-tha in Spain but ser-vay-sa in Latin American Spanish.