We have measured the critical behavior of the spontaneous magnetization as a function of temperature for $T<~{T}_{c}$ in the three-dimensional, uniaxial, dipolar-coupled ferromagnet LiHo${\mathrm{F}}_{4}$ using elastic-laser-light-scattering techniques. In the reduced-temperature range $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}<~t<~1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}1}$, we find that the logarithmically corrected mean-field power law $\frac{M(T)}{M(0)}={\mathrm{Bt}}^{\frac{1}{2}}{|\mathrm{ln}|\frac{{t}_{0}}{t}||}^{\frac{1}{3}}$ fits the data with ${T}_{c}=1.5383\ifmmode\pm\else\textpm\fi{}0.0003$ K, ${t}_{0}=0.483\ifmmode\pm\else\textpm\fi{}0.046$, and ${\ensuremath{\chi}}^{2}=1.34$. We have also fitted the data to $\frac{M(T)}{M(0)}=B{|t|}^{\frac{1}{2}}{|\mathrm{ln}|t||}^{\frac{1}{3}}[1+{C}_{1}(\mathrm{ln}\frac{|\mathrm{ln}|t||}{\mathrm{ln}|t|})+{C}_{2}(\frac{1}{\mathrm{ln}|t|})]$ in order to obtain explicitly the corrections to the leading singularities. We find in this fit that ${T}_{c}=1.5382\ifmmode\pm\else\textpm\fi{}0.0003$ K, ${C}_{1}=0.07\ifmmode\pm\else\textpm\fi{}0.3$, ${C}_{2}=0.287\ifmmode\pm\else\textpm\fi{}0.07$, and ${\ensuremath{\chi}}^{2}=1.26$. Fits to a simple power law $\frac{M(T)}{M(0)}={\mathrm{Bt}}^{\ensuremath{\beta}}$ yield ${T}_{c}=1.5370\ifmmode\pm\else\textpm\fi{}0.0002$ K, $\ensuremath{\beta}=0.355\ifmmode\pm\else\textpm\fi{}0.005$, and ${\ensuremath{\chi}}^{2}=17.2$. We also present measurements of the temperature and magnetic-field dependence of the light scattering in LiHo${\mathrm{F}}_{4}$, and the magnetic-field and wavelength dependence of the circular birefringence.