So the quickest answer is that SQL expects the same dimension of columns in each statement you try to do a UNION on. So all the first column of your SQL statements should match what you want to be in the first column of your result. Generally, they will also need to match in data type.
The column names themselves don't matter.
So to make yours work you'd do something like
SELECT the_geom, name, type, '' AS description, unit_code FROM points_of_interest
UNION ALL
SELECT the_geom, altname, '' AS type, descriptio, unitcode FROM arch_visitor_centers
UNION ALL
SELECT the_geom, name, '' AS type, '' as description, '' as unitcode FROM arch_trailheads
UNION ALL
SELECT the_geom, bldg_name, '' AS type, '' as description, '' as unitcode FROM arch_restrooms
UNION ALL
SELECT the_geom, name,'' AS type, '' as description, '' as unitcode FROM arch_parking
UNION ALL
SELECT the_geom, name,'' AS type, '' as description, '' as unitcode FROM arch_campgrounds
The result would contain
the_geom, name, type, description, unit_code
I'm assuming that type, name, description, and unit_code are all Text type variables. You can keep track of what table your rows came from by manually including a final column that just includes the table name aliased to a column. E.g.
SELECT the_geom, name, type, '' AS description, unit_code, 'points_of_interest' as source_table FROM points_of_interest
UNION ALL
SELECT the_geom, altname, '' AS type, descriptio, unitcode, 'arch_visitor_centers' as source_table FROM arch_visitor_centers
UNION ALL
SELECT the_geom, name, '' AS type, '' as description, '' as unitcode, 'arch_trailheads' as source_table FROM arch_trailheads
UNION ALL
SELECT the_geom, bldg_name, '' AS type, '' as description, '' as unitcode, 'arch_restrooms' as source_table FROM arch_restrooms
UNION ALL
SELECT the_geom, name,'' AS type, '' as description, '' as unitcode, 'arch_parking' as source_table FROM arch_parking
UNION ALL
SELECT the_geom, name,'' AS type, '' as description, '' as unitcode, 'arch_campgrounds' as source_table FROM arch_campgrounds