I am trying to set up a spreadsheet that is quite complicated and I'm
not sure if it can be done. Basically it is based on an audit sheet,
with the names in Row 13 and the amount of errors in Row 72 (so for
example it will show Alison in Row 13 and then in Row 72 it will show
5). What I'm looking to do is set up a formula to first search for a
name and then see how many errors that person has (a person may appear
more than once in the sheet)....

One way:
=SUMIF(13:13,"Alison",72:72)