strange character encoding of stored data , old script is showing them fine new one doesn't

In short, because this has been discussed a thousand times before:

1. PHP holds a string, say "漢字", encoded in UTF-8. The bytes for this are E6 BC A2 E5 AD 97.
2. It sends this string over a database connection which is set to latin1.
3. The database receives the bytes E6 BC A2 E5 AD 97, thinking those represent latin1 characters.
4. The database stores the characters æ¼¢å­ (the characters that E6 BC A2 E5 AD 97 maps to in latin1).
5. The same process reversed makes PHP receive the same bytes, which it then treats as UTF-8. The roundtrip works fine for PHP, even though the database doesn't treat the characters as it should.

So the problem here was that the database connection was set incorrectly when the data was entered into the database. You'll have to convert the data in the database to the correct characters. Try this:

SELECT CONVERT(BINARY CONVERT(field_name USING latin1) USING utf8) FROM table_name

Maybe utf8 isn't what you need here, experiment. If that works, change this into an UPDATE statement to update the data permanently.

The deceze's answer is excellent but I can add some info that may help to handle lots of records without test them manually.

If the conversion CONVERT(BINARY CONVERT(field_name USING latin1) USING utf8) fails, it print NULL instead of the field_name content.

So I use this one to find those record:

SELECT IFNULL(    CONVERT(BINARY CONVERT(field_name USING latin1) USING utf8)    , '**************************************************')FROM table_name

or this one:

SELECT id, field_name, CONVERT(BINARY CONVERT(field_name USING latin1) USING utf8)FROM table_nameWHERE CONVERT(BINARY CONVERT(field_name USING latin1) USING utf8) IS NULL

And the UPDATE with the clause to affect only records on which the conversion success:

UPDATE table_nameSETfield_name = CONVERT(BINARY CONVERT(field_name USING latin1) USING utf8mb4 )WHERECONVERT(BINARY CONVERT(field_name USING latin1) USING utf8mb4) IS NOT NULL