in this case, the significance is in making this a non-minimum phase system. Eg, the frequency magnitude response of (s+1)/(2s+1) is the same as (s-1)/(2s+1). But the phase shifts are different. the first case has a minimum phase shift, while the second case does not. This becomes very important for control systems.
There will be no real frequency with a gain of 0. the fourier transform is simply the imaginary axis of the laplace transform. (or the unit-circle of the z-transform for discrete samples). If you don't have any zeros on the axis due to the numerator, then you only need to check for zeros at inf. in this case, there are no zeros at inf, as the limit approaches 1/2.