Both "увидеть на записи" and "увидеть в записи" are grammatically correct in Russian, but they can have slightly different meanings.

"Увидеть на записи" typically suggests seeing something physically written or recorded on the document, while "увидеть в записи" can be interpreted as understanding or noticing something in the content of the document. Both phrases can be used interchangeably depending on the context, but it's important to keep in mind the slight nuance in meaning.