inconsistencies in the whole GPS methodology of measuring space and time coordinates
inconsistencies of units (meters, second) used at various places: the errors would have to be huge, indeed, so this is unlikely
subtle old-fashioned physics issues neglected by GPS measurements: the index of refraction of the troposphere and (even more importantly) ionosphere that slows down and distorts the path of GPS signals; confusing spherical Earth and geoid; neglecting gravitational effects of the Alps; neglecting magnetic fields at CERN that distort things; and so on
forgetting that 2 milliseconds isn't zero and things change (e.g. satellites move) during this short period, too
subtle special relativistic effects neglected in the GPS calculations
subtle general relativistic effects neglected in the GPS calculations
wrong model of where and when the neutrinos are actually created on the Swiss side
more radical: wrong model of the wave equation for the neutrinos (regardless of oscillations etc., neutrinos should never move information faster than light in the vacuum, but maybe we're doing some mistake about the group vs phase velocity and entanglement of the two places: recall that the difference between the phase and group velocity for these neutrinos should be negligible, around \(10^{-19}\))