My dad and I are filling out the DS-160 Visa form online. We got to where he is asked to list all of his previous employment. The problem is that he has worked in a lot of schools in the past 25 years. Would it matter, and would he risk rejection, if he didn't list all of his employment on the form?
No. The DS-160 FAQ says
enter information regarding your previous two employers only.
However, same FAQ elaborates that
Applicants may choose to bring along a separate written list of all previous employers to the visa interview for reference.
He should list as many as he remembers. Do not fret over those he does not remember. The USA is primarily concerned with working for or affiliation with terror sponsoring organizations, criminal enterprises, and terrorist organizations. He will not be refused because he worked for some school twenty years ago for a few months and forgot to include it.
How do I know? Because during my green card and citizenship process I forgot some minor companies I briefly worked for and it was not a problem. Note that green card and citizenship applications are scrutinized even more stringently than visa applications.
DS-160 FAQ mentions about previous employers in last 5 years.
For US employers, It's better to put those details where one worked with valid work petitions, tax/W2 history. For Non-US employers in last 5 years, it's better to put that information, if available.
Few Non-USCIS website to substantiate above info: Few non-USCIS websites supporting above information is as :