Hello podo,
Most people tend to think that motor current FFT is the way to go. But there are a couple of other ways, as you indicated.
In the good old days, the analoge ammeter did quite a good job in filtering away all frequencies above five or so Hz. So it was quite easy to see the small low-frequency current variations that a broken rotor bar results in. It is very similar to the frequency analysis that you get from an FFT process. Look for small periodic variations in motor current. I use a clamp-on ammeter with soft iron instrument. Works well and is not affected by PWM inverters. Hard to get these days, though.
Measuring slip and comparing to calculated slip is also a useful technique. As an example, assume that your motor has 1450 RPM rated speed at full load (50 Hz grid). The slip will be close to zero at no load and 50 RPM at full load. Now, you have to know the shaft load. So you will need to know the kW input and then multiply by efficiency AT THAT LOAD, and that is where it gets tricky. But if you arrive at, say, 70 % load, then your slip should be 35 RPM. That is, the speed shall be 1465 RPM. If you measure a much lower speed, like 1440 RPM or so, you can be sure that one or more rotor bars are broken.
A broken bar often/always shows as excess rotor temperature and if someone tells you that the shaft or the bearings are unusually hot compared to what it used to be, you should start thinking rotor bars.
The number one method (not counting FFT) is to look for slow periodic motor current variations, though.