  We consider continuous $\mathrm{SL}(2,\mathbb{R})$ valued cocycles over
general dynamical systems and discuss a variety of uniformity notions. In
particular, we provide a description of uniform one-parameter families of
continuous $\mathrm{SL}(2,\mathbb{R})$ cocycles as $G_\delta$-sets. These
results are then applied to Schr\"odinger operators with dynamically defined
potentials. In the case where the base dynamics is given by a subshift
satisfying the Boshernitzan condition, we show that for a generic continuous
sampling function, the associated Schr\"odinger cocycles are uniform for all
energies and, in the aperiodic case, the spectrum is a Cantor set of zero
Lebesgue measure.
