On a mountain you shouldn't be relying solely on GPS, you should always have map and compass as well, and sometimes they are more reliable.

GPS can be wildly inaccurate in some circumstances. In mountains the signals can sometimes be deflected by big cliffs - I tracked my ascent of Tower Ridge on Ben Nevis which showed a number of significant deviations to either side, which if they were to be believed would have placed me several hundred feet in the air above the neighbouring corrie.

However, at the scales used for leisure purposes the Ordnance Survey maps are not precise, due to scaling, projection and other differences, and printing inaccuracies. Navigation ultimately relies on relating whatever you can see around you to information your various tools can provide.

The leap second arises because we now want to measure time far more precisely than the rotation of the earth allows. GPS is just part of this.