How can there be two potentials at this point? 
In this potentiometer configuration, The blue circled junction has potentials $V$ and $E$ at the same time (Galvanometer shows no deflection), Why is this so? What conceptual error have I made?
 A: $E$ and $V$ are the potential differences between the positive and negative terminals of the two batteries, and not the potential at the circled point.
Assuming negligible resistance wires, the potential of the positive terminals of the two batteries and the circled point has to be the same since they are connected together.
Now you might ask, "what is the potential at the circled point?", to which I would answer, it depends on what point in the circuit is assigned a potential of zero volts. While technically an arbitrary decision, typically that point is one that is shared with multiple components or the negative terminal of a battery.
For example, if the negative terminal of the upper battery is assigned a potential of zero volts, then the potential at the circled point would be $V$ volts. If the potential of the negative terminal of the bottom battery is assigned a potential of zero volts, then the potential at the circled point would be $E$ volts. The potential at any point in the circuit is the voltage measured between that point and the point assigned a potential of zero volts.
Hope this helps.
