  In the fundamental quest of the rotation curve of the Milky Way, the
tangent-point (TP) method has long been the simplest way to infer velocities
for the inner, low latitude regions of the Galactic disk from observations of
the gas component. We test the validity of the method on realistic gas
distribution and kinematics of the Milky Way, using a numerical simulation of
the Galaxy. We show that the resulting velocity profile strongly deviates from
the true rotation curve of the simulation, as it overstimates it in the central
regions, and underestimates it around the bar corotation. Also, its shape
strongly depends on the orientation of the stellar bar. The discrepancies are
caused by highly non-uniform azimuthal velocities, and the systematic selection
by the TP method of high-velocity gas along the bar and spiral arms, or
low-velocity gas in less dense regions. The velocity profile is in good
agreement with the rotation curve only beyond corotation, far from massive
asymmetric structures. Therefore the observed velocity profile of the Milky Way
inferred by the TP method is expected to be very close to the true Galactic
rotation curve for 4.5<R<8 kpc. Another consequence is that the Galactic
velocity profile for R<4-4.5 kpc is very likely flawed by the non-uniform
azimuthal velocities, and does not represent the true Galactic rotation curve,
but instead local motions. The real shape of the innermost rotation curve is
probably shallower than previously thought. Using a wrong rotation curve has a
dramatic impact on the modelling of the mass distribution, in particular for
the bulge component of which derived enclosed mass within the central kpc and
scale radius are, respectively, twice and half of the actual values. We thus
strongly argue against using terminal velocities or the velocity curve from the
TP method for modelling the mass distribution of the Milky Way. (abridged)
