Sure, you have to preprocess the data and run business rules against it. That's different than running an UPDATE ... FROM statement using source data that's known to have flaws. Back to the OP - ...

So I am trying to write an update statement that uses two factors to determine the new value of the field, one of the factors is an aggregate function (COUNT). I get the error: An aggregate may not ...

A common SQL habit is to use SELECT * on a query, because it’s tedious to list all the columns you need. Plus, sometimes those columns may change over time, so why not just do things the easy way? But ...