Is there an smooth foliation of the plane which is not smoothly equivalent to a foliation $dH=0$ where H is a harmonic function without critical values?

If the answer is negative then we conclude that every smooth foliation of the plane satisfies the properties required in the following post

Finding a 1-form adapted to a smooth flow

In fact for the foliation $dH=0$ the $1\_$ form $\theta=H_y dx - H_x dy$ is the required form.