Does the depth that you plug in an appliance have an effect?
What you are describing is a poor electrical contact between the plug and socket contacts. 

The result of poor contact is high resistance. 
The result of resistance is voltage drop and heating. 


The voltage drop is given by \$ V = IR \$, where I is the current and R is the resistance so the more current the lower the voltage delivered to the appliance. Your mobile phone charger takes so little current that it won't matter. A larger load such as a heater or washing machine will suffer a much larger voltage drop and may not work properly.
The power dissipated in the poor contact is given by \$ P = I^2 R \$, where I is the current (amps) and P is the power (watts). Notice that the power increases with the square of the current so heat build-up becomes significant enough at higher currents that fire becomes a risk.