I) Right, the **differential form**  of [Gauss's law](http://en.wikipedia.org/wiki/Gauss%27s_law#Differential_form) 
$$ {\bf\nabla} \cdot{\bf E}~=~ \frac{\rho}{\varepsilon_0} $$ 
uses the relatively advanced mathematical concept of [Dirac delta distributions](http://en.wikipedia.org/wiki/Dirac_delta_function) in case of point charges

$$\rho({\bf r})~=~\sum_{i=1}^n q_i\delta^3({\bf r}-{\bf r}_i).$$

Note in particular, that it is technically wrong to claim that the Dirac delta distribution is a [function](http://en.wikipedia.org/wiki/Function_%28mathematics%29): $\mathbb{R}^3\to [0,\infty]$ that takes the value $\infty$ at the origin ${\bf r}={\bf 0}$, and zero everywhere else. It is a [generalized function](http://en.wikipedia.org/wiki/Distribution_%28mathematics%29).

II) To avoid the notion of [distributions](http://en.wikipedia.org/wiki/Distribution_%28mathematics%29), it is more safe and probably more intuitive to work with the [equivalent](http://physics.stackexchange.com/q/38404/2451) **integral form**  of [Gauss's law](http://en.wikipedia.org/wiki/Gauss%27s_law#Integral_form) 

$$ \Phi_{\bf E}~=~ \frac{Q_e}{\varepsilon_0}. $$

The corresponding [Gauss's law for magnetism](http://en.wikipedia.org/wiki/Gauss%27s_law_for_magnetism)

$$ \Phi_{\bf{B}}~=~ 0 $$

expresses (without employing double standards) the fact that there is no magnetic charge $Q_m$.