You could get rid of the cursor here too. Something like this should be pretty close.

DECLARE @CORRECTION_STATEMENT nvarchar(max)

select @CORRECTION_STATEMENT = 'UPDATE [janinetestdata].[dbo].[EDTE] set ' + Columns_To_Fix + ' = '''

+ Corrected_Value + ''' WHERE zBarcode = ' + zBarcode + ' and '

+ 'PERSON_NUMBER = ' + Person_No + ';'

from [janinetestdata].[dbo].[TEST66]

where Command = 'UPDATE'

and Person_No is not null

and Columns_To_Fix is not null

and zBarcode is not null

exec sp_executesql @CORRECTION_STATEMENT