  We demonstrate that the three dimensional incompressible
magneto-hydrodynamics (MHD) system is ill-posed due to the discontinuity of
weak solutions in a wide range of spaces. Specifically, we construct initial
data which has finite energy and is small in certain spaces, such that any
Leray-Hopf type of weak solution to the MHD system starting from this initial
data is discontinuous at time $t=0$ in such spaces. An analogous result is also
obtained for the Navier-Stokes equation which extends the previous result of
ill-posedness in $\dot B^{-1}_{\infty,\infty}$ by Cheskidov and Shvydkoy to
spaces that are not necessarily critical. The region of the spaces where the
norm inflation occurs almost touches $L^2$.
