The red square and blue rectangle (which extends fully underneath the red square) are fills on the top and bottom layers, respectively. Why would I get an unrouted net constraint here?
In my experience, Altium gets mixed up when vias are close together. When it says there is an un-routed net from via to via, try moving the vias farther apart (or make them smaller).
You can also get more info about what Altium is thinking by going to Design -> Rules... and then select Electrical - Un-routed Net - UnroutedNet. In that dialog box, uncheck the option for "Check for incomplete connections." If that makes your errors go away, then it tells you that your vias are close enough that Altium thinks they should be connected together, but somehow doesn't understand that the polygon fill is making the connection. Don't know why... seems like a bug to me.
I don't think fills count as actual copper nets, or if they do it's pretty buggy. You need to actually draw a polygon pour in order for it to work to connect components. Also, to state the obvious, the polygons need to have the same net as the objects they're supposed to be connecting. The net is set in the polygon properties.