The ground clip of your scope is connected to Earth. If anything else in your motor drive circuit is connected to Earth, this can lead to some large currents through the scope, which is noise at best, burnt fuses, traces, smoke, fire at worst.
Even if your motor drive circuit is floating, by clamping one half of the motor to Earth, you make the circuit unsymmetrical. Everything in your circuit has some capacitance to everything else in the universe, Earth being a pretty significant part of that. To change the voltage across a capacitance (such as that between any part of your circuit and Earth) some current must flow, according to:
$$ I = C \frac{dv}{dt} $$
Normally this isn't a big deal, but I'm guessing you have some relatively high voltages involved, since you have a node labeled "HV_BUS" and that's a 500V MOSFET. Normally, it's just the MTR- node that changes voltage relative to Earth significantly, and these capacitive currents are really insignificant compared to the motor currents. But when you force MTR- to be at Earth potential, now it's everything else in your circuit that's switching \$\pm500V\$ relative to Earth, and these capacitive currents are in your ground, in your control circuitry, etc.
For a simpler demonstration of problems introduced by capacitive coupling to Earth, see Why one of my multimeter shows a small voltage when only one probe is connected to AC and the other dont?
The way to work around this is to clip your scope probe to the circuit ground. If you need to measure the difference between the motor terminals, use both channels on your scope, each clipped to ground and one of the motor terminals, and use the X-Y difference function of your scope.
Or, since HV_BUS is a constant voltage from ground, you can clip your scope ground lead here only if the motor driver is floating and you are confident this won't introduce a safety hazard and just consider the voltages you measure to be negative.
One simple example
Let's say you have two scope probes. Probe A is correctly grounded to the circuit you are measuring but probe B doesn't have a ground connection. Let's also say that probe A is measuring a 1Vp-p squarewave on the circuit and probe B is looking at a DC level.
Despite scopes having a 1M\$\Omega\$ input impedance, there will be currents that flow through the probe due to the edges of the square wave - the scope input impedance is also likely to comprise 20pF capacitance (smaller for x10 probes usually).
This capacitance "takes" a pulse of current down the probe lead every time the square wave alternates causing a small volt-drop down the lead. This won't matter for probe A but, this will appear as a small "spike" on channel B's display because the glitch "becomes" in series with the probe B signal due to it being ungrounded.
If probe B were correctly grounded at the circuit this "glitch" won't be present on the scope B waveform.
What point/frequency does this become significant? I would answer that by saying just don't take short cuts. If you are probing a circuit for whatever reason, use best practise and ground both probe ends at the circuit you are measuring or expect anomalies.
If probe A is looking at 1Vp-p squarewave and probe B is looking at a 5mV analogue signal you'll have troubles on channel B.
Best Answer
The ground end of the scope probe is normally connected to AC power ground so you have to be careful. You cannot measure across two terminals if neither is connected to ground. Therefore you are correct in being suspicious of connecting the probe directly across the motor since neither motor lead may be grounded. You can try your second method but you will not be seeing the voltage across the motor but only each terminal with respect to ground. This may be OK if you are careful in interpreting the waveforms. Another method is to use the differential mode of your oscilloscope. Most 2-channel scopes can be set to display the difference in voltage of their 2 channels. If yours can do that, then connect the high end of the channel 1 probe to one motor terminal and the high end of tge channel 2 probe to the other motor terminal. If you invert channel 2 (a normal option for scopes than can display channel 1 - channel 2), and select the difference mode, the scope will display the voltage across the motor.