A lot to ponder. My 2 cents.
Baseline:
- There is only one correct scientific name (even if in flux or being disputed).
- There can be numerous correct synonyms (even if in flux or being disputed).
- There are incorrect scientific names used. [invalid] names found on taxon sites (ITIS, ...).
- Generally there is only one correct cultivar name, with a few society driven exceptions. Rosa, maybe Lilium, maybe others.
- There can be multiple correct Trade Designations. ex. Translated cv. names meet the ICNCP criteria.
The Trade and other sources:
A. There are numerous incorrect scientific names used. Just inaccurate. Not noted on taxon site (ITIS, ...).
B. There are numerous cv. names not recognized by any authority (some used by "good" growers) that are not Trade Designations (Do not meet ICNCP criteria).
In the synonym field, if we accept [invalid] after a scientific name which does not appear on a taxon site, problem A solved. Better yet [illegitimate].
If we have a 3rd field like "As Sold As", incorrect Cultivar/Trade Designations/Trade Names/Garbage Names can be added. Problem B solved.
Flaw: [illegitimate] scientific name often pared with incorrect B name.
