  Teleparallel theories of gravity have a long history. They include a special
case referred to as the Teleparallel Equivalent of General Relativity (TEGR,
aka GR$_{\|}$). Recently this theory has been generalized to f(T) gravity.
Tight constraints from observations suggest that f(T) gravity is not as robust
as initially hoped. This might hint at hitherto undiscovered problems at the
theoretical level. In this work, we point out that a generic f(T) theory can be
expected to have certain problems including superluminal propagating modes, the
presence of which can be revealed by using the characteristic equations that
govern the dynamics in f(T) gravity and/or the Hamiltonian structure of the
theory via Dirac constraint analysis. We use several examples from simpler
gauge field theories to explain how such superluminal modes could arise. We
also point out problems with the Cauchy development of a constant time
hypersurface in FLRW spacetime in f(T) gravity. The time evolution from a FLRW
(and as a special case, Minkowski spacetime) initial condition is not unique.
