If an ECM is bad what tell tell signs would surface? I still have the Q-jet carb, last year for carbs on '81, which I believe the ECM controls some settings at idle and low rpm and also transmission hookup.

Hi Tommy, 
     I have an 82 with the Cross Fire fuel injection.  The ECM controls the firing of the ignition and in the 82 fuel injection the duration of the pulse of the throttle bodies injectors and thus controlling the rich/lean fuel air mixture.
     As for failure, the module is a computer that monitors the various sensors in the engine compartment and exhaust system.  You would expect a complete failure would stop the ignition system - no spark - won't start.  You might also expect intermittent operation if the connections to the ECM are intermittent or bad. 
     I am relatively new to Corvettes but, when my Saturn computer failed the engine would not start.  The service folks popped a new computer in and all was well in my first plastic car. 
     You can get a code reader and see what codes are stored in the memory.  I got one at the local parts store for $24.  I'm sure that there are cheaper ones around.  Make sure it will read your year, make and model.  There are several codes that will come up if your ECM is bad.  Generally, these things are very reliable.  The operating conditions are in ROM (read only memory).  The codes are stored in a volatile memory that may be cleared by disconnecting the positive battery terminal for 10 to 30 seconds. 
     I think it is more likely that (if bubba has not fooled around with the ECM) you should check the sensors and associated wiring.  More experienced folks on this site might chime with better or additional info.  If you can give us more info on the nature of your problem that will help. Good luck.

The ECM for the '81 didn't really have a lot to do. It basically controlled the idle fuel mixture, the timing(to a degree[no pun intended]), and the lock-up torque converter for the trans.
So, the engine would still run, but it prolly wouldn't run well at idle, nor would it have the proper ignition timing at speed, and you may/may not have lock-up. It all depends on the failure mode of the ECM.
The ECM does use other inputs to do it's thing. It needs input from the O2 sensor(s), the TPS(in the carb), and of course an RPM signal from the distributor.
There are other functions that go thru the ECM, but most of those would have nothing, or very little, to do with the actual running of the engine.
Scanning the ECM with a scanner(or paper clip) and getting any codes it has would help point to something more specific. However, the early ECMs do NOT have the capability to "store" any codes or info. IF the "Check Engine" light is not on, there will be no codes.
hth

if the check engine light came on wile driving then went out, would not the code still be there until the car is shutoff?

The early systems did not have the capability to "store" a code. The way it works is, if the ECM "sees" an issue that requires it, it will turn the Check Eng/Service Eng light on. IF the issue goes away while driving, the light will go off, and the code will disappear. For instance, if the ECM sees an issue with the TPS(throttle position sensor) that is maybe out of spec, the light will come on, and a code will be available. If the TPS problem goes away, then the light goes off, and the code is gone also. A TPS can have a very small "bad spot", usually right at the place it would be while cruising on the highway. The accelerator pedal may stay in the area just long enough for the ECM to see it is out of whack, and turn the light on. If the TPS  bad spot is fairly large, the light may stay on for a while. Once the pedal is moved out of that particular "bad" spot, it will again start reading properly. The ECM will now receive the correct reading, and, after a certain amount of time, it will extinguish the light, and delete the code. Some problems need to be in effect for a certain amount of time, or recur several times in a certain amount of time, before a code will even set. This is why it's best to try to scan for codes while the light is on. If the light is on while driving, and you scan it, you'll be able to pull the code. If you turn the key off, even while the light is on, the code will not be stored. NOw....if you have  a "hard" failure, meaning an issue that is occurring just by turning the key on, then you'll be able to see that particular code. For instance, if you were to unplug the flat connector going to the distributor, and turn the key on, the ECM would recognize that it doesn't get any feedback from the ESC system, and it would set a code for that.
Hope that helps.
Later GM systems(I think '84-up) do have the ability to store codes, even if the light goes out, and the problem is not present at the time, but the '81 will not.