I am unsure why the multirow is not vertically centered
Your \labentry macro is defined as follows:
\newcommand{\labentry}[1]{\multirow{3}{*}{\parbox{1.7in}{\raggedright#1}}}
Observe that it's set up to span a fixed number of rows: 3.
In the body of the longtable, there's the instruction
\labentry{Check-in/Safety Rules}
The vertical alignment issue arises because the material in the immediately adjacent cell spans only 2 rows, not 3 rows. One way to fix this is to redefine \labentry so that it's contents span only 2 rows, not 3. Or, redefine labentry so that it takes two arguments rather than 1; use the second argument to indicate the number of rows it's supposed to span.
Better still: Don't use \multirow at all here. There is simply no way that readers will not understand how the information in the "Labs" column is related to the information in the preceding "Sections covered" column.
Addendum to address the OP's follow-up comment:
I am using multirow, simply because I would like the "Labs" column to be vertically centered. Purely for aesthetics.
Be careful not to let your sense of aesthetics create unwanted ambiguity. To truly center the line "Check-in/Safety Rules" in the final column with regard to the information contained in the preceding columns, you should actually set aside 5 rows, not just 3 rows, in the \multirow directive. That's because the material in the preceding columns spans, well, 5 rows once you allow for the automatically generated line breaks.
If you do set aside 5 rows in the first argument of \multirow, there's a new and rather serious problem: How do you make sure that the students understand that "Check-in/Safety Rules" pertains to all three dates and not just to the middle date (Jan 11)? As the first half of the table shown below demonstrates, I (for one, and I don't think I'm alone) would immediately assume that "Check-in/Safety Rules" pertains only to the middle date. To truly avoid creating such an ambiguity, I think it's necessary to ditch the \multirow approach and repeat the salient information in the final column as often as is needed.

\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage[justification=centering,font=bf]{caption} % <--- new
\usepackage{longtable,array,booktabs,multirow}
\newcommand{\mod}[2]{Module~\##1 --- #2}
%% I've modified the following macro to take 2 arguments
\newcommand{\labentry}[2]{\multirow{#1}{*}{\parbox{1.6in}{\raggedright #2}}}
\begin{document}
\begin{longtable}{@{} lll
>{\raggedright}p{2.16in}
>{\raggedright\arraybackslash}p{1.6in} @{}}
\caption*{Chemistry 1407 Lecture/Lab Schedule\\Spring 2017}\\
\toprule
\textbf{Lecture \#} & \textbf{Weekday} & \textbf{Date} & \textbf{Sections Covered} & \textbf{Labs} \\
\cmidrule(r){1-1} \cmidrule(lr){2-3} \cmidrule(lr){4-4} \cmidrule(l){5-5}
\endfirsthead
\toprule
\textbf{Lecture \#} & \textbf{Weekday} & \textbf{Date} & \textbf{Sections Covered} & \textbf{Labs} \\
\cmidrule(r){1-1} \cmidrule(lr){2-3} \cmidrule(lr){4-4} \cmidrule(l){5-5}
\endhead
\bottomrule
\endfoot
-- & Monday & 1--09 & Read D2L Introduction \& OWL Registration
& \labentry{5}{Check-in/Safety Rules}\\
1 & Wednesday & 1--11 & \mod{1}{Section 1.7} & \\
2 & Friday & 1--13 & \mod{1}{Sections 1.5--1.6, 1.9} & \\
\midrule
-- & Monday & 1--09 & Read D2L Introduction \& OWL Registration
& Check-in/Safety Rules\\
1 & Wednesday & 1--11 & \mod{1}{Section 1.7} & see above\\ % note the "see above" instructions
2 & Friday & 1--13 & \mod{1}{Sections 1.5--1.6, 1.9} & see above\\
\end{longtable}
\end{document}
\labentrymacro isn't set up correctly: It is set to span 3 rows, yet the multi-line cell that's adjacent to the instance of\labentryspans only 2 rows. The\multirowdirective is working exactly as it is supposed to. What needs to be fixed, then, is the structure of the\labentrymacro. – Mico Jan 08 '17 at 21:48\modmacro should be defined as\newcommand{\mod}[2]{Module \##1 -- #2}, i.e., without the space after\#. – Mico Jan 08 '17 at 22:10\modafter posting and fixed that already – J M Jan 08 '17 at 22:15\mod: as soon as you loadamsmathyou'll know why. I agree with Mico that the vertical centering only for the last column is unnecessary (I'd even say it's wrong). – egreg Jan 08 '17 at 22:24amsmathownmodcommand. Thank you to @hakaze for the info. You are entitled to your personal preference @egreg for the visuals of this, but for this purpose and how student's are expecting it to look, I will stick with it vertically centered. – J M Jan 08 '17 at 22:55