This will only select fields which are not valid UTF-8:
SELECT * FROM table
WHERE CONVERT(field USING binary) RLIKE '([\\xC0-\\xC1]|[\\xF5-\\xFF]|\\xE0[\\x80-\\x9F]|\\xF0[\\x80-\\x8F]|[\\xC2-\\xDF](?![\\x80-\\xBF])|[\\xE0-\\xEF](?![\\x80-\\xBF]{2})|[\\xF0-\\xF4](?![\\x80-\\xBF]{3})|(?<=[\\x00-\\x7F\\xF5-\\xFF])[\\x80-\\xBF]|(?<![\\xC2-\\xDF]|[\\xE0-\\xEF]|[\\xE0-\\xEF][\\x80-\\xBF]|[\\xF0-\\xF4]|[\\xF0-\\xF4][\\x80-\\xBF]|[\\xF0-\\xF4][\\x80-\\xBF]{2})[\\x80-\\xBF]|(?<=[\\xE0-\\xEF])[\\x80-\\xBF](?![\\x80-\\xBF])|(?<=[\\xF0-\\xF4])[\\x80-\\xBF](?![\\x80-\\xBF]{2})|(?<=[\\xF0-\\xF4][\\x80-\\xBF])[\\x80-\\xBF](?![\\x80-\\xBF]))';
(The regex is from https://stackoverflow.com/a/11709412/323407.
Requires PCRE regex support. MySQL does not have that out of the box but MariaDB 10.0.5+ does. For MySQL maybe you can use lib_mysqludf_preg.)
Not sure if this is what the question is asking for - if someone stored their information in an encoding that is not UTF-8 but happens to output byte sequences that are valid UTF-8, this will not help with that (and I don't think a 100% reliable solution exists - if you know the specific encoding and language, you can maybe look for common corrupted character sequences). But it's useful for finding input that's definitely not UTF-8.
(This assumes the text is stored in a format where invalid UTF-8 is even possible, e.g. binary.)