Electrical – Trip switch goes off 50% of the time when turning off an appliance

It sounds to me like the most plausible thing is that the builders installed some nails, screws or other fasteners to the wall or ceiling and punctured through some electrical wire causing an intermittent short circuit.

If the switching on of the kitchen light switch is what sets it off then you have already isolated it to a particular area of your house. It has to be a rather heavy duty short to cause it to trip your whole house breaker!!

Another thing to consider is that a fault of this type could very well be pretty dangerous. If the short was one that caused there to be live power present on the metal parts of any appliances or light fixtures this could be a very serious shock hazard.

There are tools that professionals can use to try to help find where shorts are located. Due to the potential serious safety issue involved with this I would strongly suggest that you get a professional electrician out to look into this problem as soon as possible. One reason for the urgency is that the short, where ever it is, may not be enough to always trip your whole house breaker but on the times where the breaker has not tripped the short could very well be generating a very hot connection which could lead a fire or burned out wiring. Take care of that call today.

Assuming the light itself isn't bad, then the combination of a dim light and the dishwasher making it go out sounds like a break in a wire or a corroded connection. A break or corrosion can allow enough current to pass to light the bulb dimly, but when a higher current is called for the resistance of the break or corrosion goes up, causing an apparent total failure.

See https://diy.stackexchange.com/a/27285/82