I just started at a new company. During the last pay period, I arrived one hour late to work (after calling in to explain) due to car trouble. When I received my first pay check, my pay was docked for that one hour.

I am a exempt salaried employee? Is this legal?

No. The only circumstance in which an exempt employee can have their salary docked in less than full day increments is if the time is attributable to FMLA. Which this is not.

They CAN require that you take vacation, sick or personal time for that hour, and they can discipline you for being late regardless of whether you called in or not. But they cannot dock your salary.

You can file a complaint with the CO DOL.

Not unless you work for a government entity. Exempt employees can only be docked salary for a partial day absence under very limited circumstances, and this is not one of them.
http://www.dol.gov/dol/allcfr/ESA/Title_29/Part_541/29CFR541.118.htm

Thanks for your help. This is the best website I have come across in some time.

So, they have to take time out of my personal time? They can't just dock my paycheck, right?

They can substitute your salary with any paid time off you have, including personal time, if that is the company policy. You just can't be shorted your total pay.

So, in this same vein, if I am ever ill and must leave work at some point during the day, I get paid for the full day?

Yes, although they can deduct the time from any paid leave that is provided. This assumes that the illness you leave work for is NOT covered under FMLA - FMLA time does not have to be paid EVER and is an exception to the regulation that says if you work any part of the day, you have to be paid for the whole day.