For an in-game team, any type disadvantages can be off set by over-leveling your Pokemon.
However, generally, you want to make sure that your types has good synergy with each other. That is to say, if your Pokemon is weak to a particular type, you should be able to safely switch in to another Pokemon that can resist that particular type. For example, it's perfectly alright to have two Pokemon of the Rock/Ground typing, as long as you have at least one Pokemon that can resist Water or Grass moves (usually your own Water or Grass type respectively)
As such I don't see too many glaring weaknesses that would cause trouble for your playthrough.
That said, you're in desperate need to update your movesets asap. The moves you're using work reasonably well in the earlier parts of the game, but the base power of most of your moves is sub-par for stronger opponents. Make sure that you have the strongest possible moves (Crunch over Bite, for example, or Surf over Water Pulse) before facing tougher opponents.
One thing you want to avoid is having moves of the same type. Having both Flamethrower and Fire wheel isn't a very good idea - Flamethrower is superior in every way, and the difference in damage dealt for Pokemon that are Physically or Specially defensive is small enough for you to focus on type coverage, specially since you're one Pokemon short of a full team. Try to use stronger, more diverse moves to cover as many of your weaknesses and hit as many opposing Pokemon as strongly as possible.
Cheers and good luck on your play through!