What are the blue dots/blobs at my wire connection point?

That blue dot indicates an equipotential conflict.

DesignSpark Electrical will number each "node" with an equipotential number, and anything that is connected along that same node will want to have the same equipotential number. If you have 2 different equipotential nodes that you somehow link up (number your wires for instance, and then later connect 2 nodes with a different number with a wire), it creates an equipotential numbering conflict. To solve this, right click anywhere on the node and choose "solve equipotential conflict" and choose the number you want representing the node.

You can also choose to disable highlighting these conflicts though Project configuration->Graphic. The 'blue blob' will not show up then.