Why does Mg react vigorously in NaCl solution and less so in water?
It would still be the same reaction.

\begin{align}
\ce{Mg (s) &amp;-&gt; Mg^2+ + 2 e-} &amp; E^\circ&amp;=\pu{2.36 V}\\
\ce{2 e- + 2H2O (l) &amp;-&gt; H2 (g) + 2OH-} &amp; E^\circ&amp;=\pu{-0.828 V} \times 2
\end{align}

The combined reaction would be spontaneous ($E &gt; 0$), but $\ce{Mg(OH)2 (s)}$ is highly insoluble, 
\begin{align}
\ce{Mg(OH)2 (s) &amp;&lt;=&gt; Mg^2+ (aq)  + 2OH- (aq)}, &amp; 
K_\mathrm{sp}=7.1 \times 10^{-12},
\end{align}
leaving the solution insufficient ions to conduct the electrons necessary to fast complete the reaction (despite of the escaping hydrogen gas). 
$$\ce{Mg (s) + 2H2O (l) -&gt; H2 (g) + Mg(OH)2 (s)}$$

This is like an electrochemical cell with no salt bridge (or bridge with only de-ionized water). Hence a little salt ions would accelerate the reaction forward.

In contrast, calcium solid, having comparable standard reduction potential, will undergo a similar redox reaction in water and needs no help for additional ions because $\ce{Ca(OH)2 (s)}$ is about a million times more soluble ($K_\mathrm{sp}=6.5 \times 10^{-6}$) than magnesium hydroxide, providing sufficient free ions in the solution to drive the vigorous release of hydrogen gas. (There are a couple of YouTube video demos.)