Definitely clean it up. It doesn't look to be in too bad of condition, just rusted and patina'd from years of exposure to the air and lack of use. Looks like it could use a new set of jaws. I'm sure a good clean up, re-painting, and re-greasing of the contact parts may all that needs to be in order.
I somewhat agree with post #4 above from balane. Most (many) Columbian vises were your typical consumer grade hardware store, farm/ranch store variety of the day. Typically bought and used by the average joe, also by the rancher or farmer of the day to be used in their farm workshops. Somewhat like the vises we see at home centers these days. Not saying that Columbian was a bad piece of ****, but many weren't the average industrial grade you'd find in a professional mechanics shop or in a machinist shop, or a factory of the era.