Yes, you can view and edit all the attributes for all objects in a base layer at once via the Attribute Table. Select the Base layer containing the objects of interest and click Map Tools | Layer Tools | Open Attribute Table.
The Attribute Table is modal and can be up on the screen at the same time you perform other tasks in Surfer. If you have multiple base layers in your map, you can open an Attribute Table for each layer if you wish. Changes made in the Attribute Table are immediately applied to the objects in the map (and vice versa), which you can see if you select an object and view the Info page in the Properties window.
Updated October 24, 2017