Table of Contents formatting issue

It is always wrong to have \\ at the end of a paragraph (and forcing a line break at the send of a section heading is particularly weird, as you see from your output)

TeX does warn about both the table of contents and the main heading

Underfull \hbox (badness 10000) in paragraph at lines 1--1
Underfull \hbox (badness 10000) in paragraph at lines 19--19

note 10000 is the maximum badness.

as you have double spaced the table, the spacing above may look a little tight so you could correct with \bigskip for example.

\documentclass{article}
\usepackage[left = 2.54 cm, right = 2.54 cm, top = 2.54 cm, bottom = 2.54 cm]{geometry}
\usepackage{titling}
\usepackage{array}
\usepackage{multirow}
\usepackage{amsmath}
\usepackage{amssymb}


\setlength{\tabcolsep}{24 pt}
\renewcommand{\arraystretch}{2}

\begin{document}

\tableofcontents

\newpage

\section{Discrete Uniform Distribution}

\begin{flushleft}
\bigskip
\begin{tabular}{@{}>{\bfseries}l l}
Abbreviation & DiscUnif$(n)$ \\
Type & Discrete \\
Rationale & Equally likely outcomes \\
Sample Space & $[1, n]\ \forall\ n \in \mathbb{Z^+}$ \\
Probability Mass Function & $f(x) = \frac 1 n\ \forall\ x \in \mathbb{Z^+}$ \\
\multirow{2}{*}{Moments} & $E(X) = \frac {n + 1} 2$ \\
& $Var(X) = \frac {n^2 - 1} {12}$ \\
\end{tabular}  
\end{flushleft}


\end{document}

If you want to ajust the spacing after all sections not just this one, you can copy the lines from article

\makeatletter
\renewcommand\section{\@startsection {section}{1}{\z@}%
                                   {-3.5ex \@plus -1ex \@minus -.2ex}%
                                   {2.3ex \@plus.2ex}%<<<
                                   {\normalfont\Large\bfseries}}
\makeatother

and adjust the value from 3.5ex to whatever size you want eg 12pt for the default baseline for the 10pt font. (negate the values to suppress indentation)

Normally do this in teh preamble but here I do it mid document to show the difference, and making it 24pt (twice baseline) to be more visible as there is not much difference between 2.3ex and one baselineskip.

\documentclass{article}

\begin{document}

\section{Discrete Uniform Distribution}

text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 

\section{Something else}

text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 


\makeatletter
\renewcommand\section{\@startsection {section}{1}{\z@}%
                                   {-3.5ex \@plus -1ex \@minus -.2ex}%
                                   {24pt \@plus 2pt}% {2.3ex \@plus.2ex}
                                   {\normalfont\Large\bfseries}}
\makeatother




\section{Discrete Uniform Distribution}

text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 

\section{Something else}

text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 
text text text text text text text text text 

\end{document}