Atra du evarinya ono varda.
No, of course not. Why, it even gives them a lot of advantage over their weaknesses! For instance, Tangrowth - a pure grass-type, is not completely useless against ALL of its weaknesses as it is able to learn Rock Slide - a rock-type move, which counters fire, ice, bug AND flying types.
This does get a tad annoying though as the opponent might come out with a move that can KO your pokemon which is super-effective against it. Surprise surprise. :/
Well, it's a double-edged sword. Use it to its full potential but prepare to face it as well.