Vertical alignment of degree unit and other elements in table

You can make \cup to align with , with the help of boxes:

\documentclass{article}
\usepackage{siunitx}
\usepackage{gensymb}
\usepackage{dcolumn}
\usepackage{multirow}
\usepackage{booktabs}
\usepackage{calc}   %% provides \widthof

\begin{document}

\begin{table}
\centering
\begin{tabular}{cS[table-format=3,table-space-text-post=\si{\degree}]r}
\toprule
\rule[-0.6em]{0pt}{1.7em} Elevation range & \multicolumn{1}{c}{Azimuth resolution} & \multicolumn{1}{c}{$N$} \\ \hline
\rule{0pt}{1.4em} \makebox[\widthof{$(-60\degree,-40\degree)$}][r]{$[-40\degree$}$,$
\makebox[\widthof{$(40\degree,60\degree)$}][l]{$40\degree]$}             & 5\si{\degree}     & 1224 \\
    $(-60\degree,-40\degree) \cup (40\degree,60\degree)$ & 8\si{\degree}  & 270 \\
    $(-70\degree,-60\degree] \cup [60\degree,70\degree)$ & 10\si{\degree}  & 144 \\
    $(-80\degree,-70\degree] \cup [70\degree,80\degree)$ & 15\si{\degree}  & 96  \\
    $(-90\degree,-80\degree] \cup [80\degree,90\degree)$ & 30\si{\degree}  & 48  \\
\rule[-0.5em]{0pt}{0.5em} \makebox[\widthof{$(-60\degree,-40\degree)$}][r]{$-90\degree$}$,$
\makebox[\widthof{$(40\degree,60\degree)$}][l]{$90\degree$}        & 360\si{\degree} & 2   \\
\bottomrule
\end{tabular}
\end{table}

\end{document}

With siunitx you can have an easier input; I'd prefer \si{\degree} to \degree.

\documentclass{article}
\usepackage{siunitx}
\usepackage{booktabs}

\begin{document}

\begin{tabular}{
  c
  S[table-format=3,
    table-space-text-post=\si{\degree}
   ]<{\si{\degree}}
  S[table-format=4]
}
\toprule
Elevation range & \multicolumn{1}{c}{Azimuth resolution} & {$N$} \\
\midrule
$[\SI{-40}{\degree},\SI{40}{\degree}]$      &   5 & 1224 \\
$(\SI{-60}{\degree},\SI{-40}{\degree}) \cup 
  (\SI{40}{\degree},\SI{60}{\degree})$      &   8 &  270 \\
$(\SI{-70}{\degree},\SI{-60}{\degree}] \cup
  [\SI{60}{\degree},\SI{70}{\degree})$      &  10 &  144 \\
$(\SI{-80}{\degree},\SI{-70}{\degree}] \cup
  [\SI{70}{\degree},\SI{80}{\degree})$      &  15 &   96 \\
$(\SI{-90}{\degree},\SI{-80}{\degree}] \cup
  [\SI{80}{\degree},\SI{90}{\degree})$      &  30 &   48 \\
$\SI{-90}{\degree},\SI{90}{\degree}$        & 360 &    2 \\
\bottomrule
\end{tabular}

\end{document}

Using the experimental tabstackengine package introduced at Writing a table with equally spaced columns, based on the widest column, you can achieve what you requested.

The package extends the stackengine package to allow tabbing.

I changed the tab and end-of-align characters for tabstackengine from & and \\ to * and /, so as not to conflict with tabular.

\documentclass{article}
\usepackage{siunitx}
\usepackage{gensymb}
\usepackage{dcolumn}
\usepackage{multirow}
\usepackage{booktabs}
\usepackage{tabstackengine}
\setstackEOL{/}
\setstackTAB{*}
\strutlongstacks{T}
\setstackgap{L}{12pt}
\stackMath
\begin{document}
\begin{table}
\centering
\begin{tabular}{ccr}
\toprule
\rule[-0.6em]{0pt}{1.7em} Elevation range & Azimuth resolution & \multicolumn{1}{c}{$N$} \\ \midrule
\alignLongstack{%
  [-40\degree\!\!\!*\,\,,40\degree]/
  (-60\degree,-40\degree) *\cup (40\degree,60\degree)/
  (-70\degree,-60\degree] *\cup [60\degree,70\degree)/
  (-80\degree,-70\degree] *\cup [70\degree,80\degree)/
  (-80\degree,-70\degree] *\cup [70\degree,80\degree)/
  -90\degree\!\!\!*\,\,,90\degree
}
&\Longstack[r]{5^\circ/8^\circ/10^\circ/15^\circ/30^\circ/360^\circ}%
&\Longstack[r]{1224/270/144/96/48/2}
\\
\bottomrule
\end{tabular}
\end{table}
\end{document}