I agree, it does seem like we're stuck between a rock and a hard place with regard to the competitiveness of our exports and managing inflation. However, I think that's always the case with monetary (or even mining) policy. It's the competing benefits and drawbacks of easy versus valuable money that result in a compromise. It certainly hasn't been handled perfectly over the last few decades, but I would disagree that this catch-22 was brought on by QE.
Just my two cents
Thats true, I guess if were looking at it from a broader perspective its more accurate to say that QE further exacerbated an ongoing problem, mismanagement of the currency.