Error if no match on join

Problem 1 - If there are any new Cost Centers that show up in the main table's Excel file that are not in the lookup table, I want the dashboard to throw an error

When the correspoding values don't exist in Lookup table, all values from Lookup table will be null. 

Then you can check for the existence of the null in any field of your choice (choose a field which can't be null) and mark error in the custom column.

Note, you can also check just before expanding your result by Table.IsEmpty as well.

if Table.IsEmpty([Column] then "Fail" else "Pass"

2. if there's a way to also throw an error if a table has a particular column with duplicate values

You will need to group the table and take count and do a self merge to take count in a separate column. 

Create a custom column to say if count > 1, then duplicate.

Hence, in a custom column you can say

= if [Column]=null then "Fail" else "Pass"

Edit - Another approach is to use following

if List.Count(List.PositionOf(Source[Letters],[Letters],Occurrence.All))>1 then "Duplicate" else "Not Duplicate"

All these techniques I have demonstrated in following file - https://1drv.ms/x/s!Akd5y6ruJhvhuSOtm_KabLBuzL7F?e=34HFkh