Would it be a bad idea to take nyquil before going to the dentist?

Yes. Nuquil should be used at bedtime. If you are taking this during the daytime you may be too drousy to function well. If your cold symptoms are severe you do not want to spread your germs to anyone else so stay home. If you are taking this because you are apprehensive about the dentist, talk to your dentist about other options that can help you during dental visits.
Inform your dentist. Medications like nyquil even though over the counter, still alter your body chemistry. This may adversly effect how medications your dentist uses affects your body. It could be dangerous... There are safer methods of anxiety control, talk to your dentist.
Ativan (lorazepam) = much better. This is simple and works well. Take a low dose 30 minutes before an appointment. Other items are available that are much more complex.