When a custom field of type "note" (i.e. a field that uses textarea for input) occurs as a searchable field in a profile, the profile search form displays a textarea for searching the field. I suggest this should be a single-line text field.
Also the search on note fields defaults to "=" as the search operator, changing to "like" if the search text contains a "%". Perhaps the behaviour for searches on alphanumeric fields should be more like "Complete OR partial Contact Name", defaulting to "like". It is difficult to think of a case where one would want to do an exact-match search on a textarea field.