It is useful to know that pokemon's weaknesses are roughly divided into three categories: special (for physical attacks) and special (for special attacks). Then there are other types that are similar, but not quite the same. This means you don't have to read a lot into weaknesses. So we'll focus on the special side.

You could say that damage type is represented in the anime by a small tile. That tile has three colors: blue, yellow, and red. That represents the physical, special, and special respectively.

Let's take a look at what each color represents:

Yellow is for a Special Attack Pokémon

is for a Special Attack Pokémon Red is for a Special Attack Pokémon that has "learned" a Physical attack