Sorry, but you issue disclosure statements to people, you don't work for homeland security.
If they have EVER been arrested, (doesn't matter if they were convicted or not), they cannot use visa waiver option.
driving offences DO count, unless you did NOT attend court.
The US WILL take a caution for drugs seriously, especially if it's recent, conviction / fine or not. It's illegal.
They should have applied for a visa, but won't have time now, and will have to hope they can bluff it at immigration, and no-one will ever know.
Did you think the US would turn a blind eye to the fact you drove with no insurance, or licence, and take drugs ?