Can I obtain a marriage certificate from the local vital records office?

Yes, if the marriage took place in Utah since 1978. Otherwise, you must contact the county clerks office in the county in which you applied for your license.

Can I obtain a certificate of divorce from the local vital records office?

Yes, if the divorce took place in Utah since 1978. Otherwise, you will need to contact the county court in which the divorce was granted.

Can I obtain birth, death, marriage, divorce certificates for events that took place in another state from the local vital records office?

No, you must apply to that state. Please try this website for obtaining information about records kept by other states:
http://www.vitalchek.com or call 1-800-255-2414.