My pence:
1) Understand the basic principal that you are dealing with. In a normal home wiring system, whenever current flows to a load, there is a bit of 'voltage drop', voltage lost to the resistance in the circuit feeding the load. The greater the current flow, the greater the voltage drop. The greater the resistance, the greater the drop. When a single circuit feeds several loads, then all of these loads will see the voltage drop, even if most of the current is being used by only one of the loads.
Voltage drop is _inescapable_, you will _always_ have some voltage drop in the system. In a well designed system, the voltage drop will not be significant, meaning that it will be smaller than the loads (and the customer) cares about, but it will still be there.
2) Understand what causes resistance. Simply having wire will mean some resistance. The longer the wire run to the panel, and the greater the resistance. The longer the service conductor run back to the supply transformer, the greater the resistance. But defects in the wiring can cause resistance as well. Not only are these annoying in terms of dimming or flickering lights, these are a fire hazard. A loose wire making poor contact can show significant resistance. A partial break in a wire can cause significant resistance.
3) Understand your loads and load sensitivity. A motor starting draws considerable current for a short period of time. This dynamic effect can make voltage drop problems very noticeable. A fridge might use 1.5A when running, but 10A when starting. Lights, in particular _dimmer fed_ lights, can be very sensitive to voltage drop. For this reason, it is often considered _good design_ to separate lights and receptacle circuits.
4) Understand the code issues involved. In general, lights are permitted on a circuit with receptacles, and a fridge plugged into such a circuit can be expected to cause a bit of dimming on these lights. Not a good idea, but possibly permitted. _However_, and this is important, the rules are different in kitchens. So called 'small appliance branch circuits' are required to feed most or all of the receptacles in kitchens, including receptacles for the fridge. Lights are not permitted on this circuit. If the fridge is plugged in where a normal fridge is expected, and it is on the same circuit as the lights, then this is a flaw in the wiring. The wiring may be perfectly safe, and the voltage drop no more than expected for the loading and length of wire, but this is still something you will have to fix. If, on the other hand, the fridge is out in the hallway, plugged into a hallway receptacle, then it might be entirely legal for the lights to share that circuit.
5) For diagnostics, I would first isolate the circuit that the fridge is on. Is this branch circuit shared with the lights? Should it be?
If the fridge is not on the same branch circuit as the lights, then go down the chain; at what point _is_ the circuit shared? At a subpanel? At the main panel? Look for sources of excessive resistance in these shared circuits.
Hope this helps.
-Jon