To make the first two minipages line up, use the [t] option to align them both at the top vertically.
I wasn't exactly sure what you meant about the third one being indented. If I had to guess though, it's probably that a space is being put in because you didn't comment out the linefeed at the end of the \vspace command. Might as well put in the \noindent command as well.
Try something like:
Code: Select all
\documentclass{article}
\begin{document}
\noindent%
\begin{minipage}[t]{0.5\textwidth}
\begin{flushleft}
\normalsize
\textbf{Industry Mentors:}\\
Person \#1 \\
Person \#2\\
Person \#3 \\
\end{flushleft}
\end{minipage}
\begin{minipage}[t]{0.5\textwidth}
\begin{flushright}
\normalsize
\textbf{Academic Mentor}\\
Person \#4
\end{flushright}
\end{minipage}
\vspace{0.5cm}%
\noindent%
\begin{minipage}[t]{0.5\textwidth}
\begin{flushleft}
\normalsize \textbf{Student Researchers:}\\
Person \#5 (project manager)\\
Person \#6\\
Person \#7\\
Person \#8\\
\end{flushleft}
\end{minipage}
\end{document}
However, since you didn't provide a full, compiliable example, it may well be that there are differences between what I have here and what you had in mind. (Your code used # where it needs \#, and there's a stray { or a missing } on one of the lines.)