You can create a
stored procedure in SQL, assuming you are using SQL, to accept the
inspectionnumber as a parameter.
The Stored
Procedure would only need to insert a record in a table with a date printed
value.
If you then
include the SP in your report, and you run the report, it will insert a record
into the table.
However, like
lockwelle mentioned, this would only keep track of the fact that the report was
run, not printed. Unless you control the printing engine with something like a
dot net application.