Potential problems if I only ground one probe of my oscilloscope?
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.