You are stuck with looking at all rows.
LIKE '%...' cannot use an index because of the leading wildcard
REGEXP can do all the testing in one try, versus multiple LIKEs, so it might be faster
AND NOT (...) does not help
OR does not help
FULLTEXT can't be very helpful because of the 'negative' testing.
- etc.
I recommend this:
AND j.Note IS NOT NULL
AND j.Note REGEXP 'audit|discrepancy|returns|shipment error|inventory adjustment'
If Note has lots of NULLs, then INDEX(Note) may help by avoiding the NULLs.
Here's another approach: As you insert rows, categorize them as "audit" or ... Then have another column (perhaps a SET) that flags which categories each Note belongs to.
If each Note belongs to only one category, then use ENUM and index it. If not, testing the SET would be a little faster than LIKEs or REGEXP.