In contrast to an ordinary voltmeter, the input of an oscilloscope generally has one side (GND) connected to ground via the mains lead. In certain situations this can be very problematic. When the measuring probe is connected to a circuit that is also connected to ground, there is a chance that a short is introduced in the circuit. That the circuit, and hence the measurement, is affected by this is the least of your problems. If you were taking measurements from high current or high voltage (valve equipment) circuits, the outcome could be extremely dangerous!
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