The CA notary manual (https://notary.cdn.sos.ca.gov/forms/notary-handbook-2018.pdf) lists the requirement on page 9.
As far as the dates are concerned, it’s the date of notarization and the description of the document. If there are no dates with signatures, The date, in the journal, is important solely as part of the description of the document (and its status).
I don’t see a problem with either Wite-out or crossing out of errors; the journal is your own personal record o what you did; when needed, it is generally accompanied by an affidavit certifying it’s authenticity (so corrections do not matter). If an entry is horribly incorrect/there should be no problem with a ‘X-out’ and new entry following. The entries must, however, be sequential (in order).
If a document has undated signatures (and I’m willing to deal with it), I’d put something like “deed in leiu, undated” in the description or notes.
Obviously, any notarization should be dated (On this, the xx day of xxx, 201x). I’d refuse any job requiring anything else.
The notary, in my opinion, does not have liability concerning the date issue if there is no notarial act (so criminal issues are off the table), however, a plaintiff could still claim a signing agent had a duty to require that all documents be dated. An attorney, or insurer, should be consulted.
I do have concerns with undated documents, because they’re actually prima facie (‘on their face’, or from the moment of their appearance) fraudulent. If a different date is put in later, it may be clearly established (i.e.: by lack of presence) that the signer could not have executed the document.
FYI, I am NY/NJ notary, but I looked at the above CA Notary handbook for supporting information.
Hope this helps.
HWB.