how bad does 30-day late hurt? how long does it hurt?

[afjock21]

for auto loan AND credit card...

[boomhower]

One hurts, two hurts a lot.  The effect will lessen with time.  If the accounts had previously had a long history of positive payments and usage you may try writing a good will letter and see if they will remove them. 

[guiness56]

A single 30 day late is a minor derogatory and you score should recover fairly quickly.  The late itself will stop impacting your score around 2 years.