Are you sure the query isn't working? Try:
SELECT TOP 100 '~'+ t.notes +'~'
FROM TABLE1 t
TOP 100
will limit the results to the first 100 rows, enough to get an idea if there's really a space in the output. If there is, and RTRIM/LTRIM is not removing it - then you aren't dealing with a whitespace character. In that case, try:
UPDATE TABLE1
SET notes = REPLACE(notes,
SUBSTRING(notes, PATINDEX('%[^a-zA-Z0-9 '''''']%', notes), 1),
'')
WHERE PATINDEX('%[^a-zA-Z0-9 '''''']%', notes) <> 0
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