What have I used a scope for, engineering-wise?
* Ensuring that pulses have a fast enough transition in a remote sensing application, where a semi-passive input circuit supplies a small current over a lopng line in the presence of line voltage.
* Making sure that output stages are being driven properly. (solenoid drivers, switching supplies, audio amplifiers, motor drivers, etc etc)
* Watching communication busses for slew rate and glitches (and with the new capabilities of even simple digital scopes, doing simple protocol debugging - of course the new scopes can do a lot of heavy lifting there that used to take building circuits to decode the buss to watch it work)
* Checking that LCD drive signals really are always exactly 50% in simple arrangements, and with at least two traces, depending, checking the switching voltages on a muxed one.
* Simple logic analysis of a digital circuit, is the clock alighed properly with the signal to be clocked in? Does the PWM go all the way from off to on as you vary the range?
* In any servo circuit (motor control, power supplies of the regulated persuasion, etc) is the contro,. of the circuit calm and controlled? Or is it unstable and oscillating around the center of the control voltage, and losing energy to switching losses that it needn't)
* When any sort of inductive load, are the freewheeling clamps doing the job of keeping the output devices from blowing up? (A more general case I've already stated above indirectly)
* Are unwanted signals in a circuit from adjacent signals? Parallel wires will tend to couple a signal in one wire onto other adjacent ones.
* Is power supply instability causing the circuit to misbehave when loaded to its' maximum?
* Where is signal loss happening in a chain of amplifier stages? (Less of a problem in the IC age, perhaps but still a valid problem)
Anytime I develop a circuit, I just "have to" watch it work. If I can't see it working, even if it works right off the bat, I get a little twitchy about it.
And once you have enough experience, to know what a circuit should be doing, the same thinking applies. And when you get a broken circuit that used to work, while static checking is often faster (e.g. are the caps open in a switcher, is often the best first test, with the circuit off) sometimes you gotta see it working in real time.
(THis is my first post in this forum, but I can't resist chiming in LOL even if I'm mostly repating things others have said)