Motz I am so glad to read this, this thread was starting to make sound like very few are getting important training like this.
During my training I was put through consecutive circuits with all flight instruments covered up, then with the gradual introduction of further failures such as flaps. It culminated in an engine failure on late cross wind with a return to the strip I had taken off from for a no instrument, flapless, engineless, downwind landing. Did all this have me sweating - YES. But was I having fun - Hell Yeah!!! More important though was the confidence that I gained in knowing that even with all the failures if you just fly attitude and power and don't panic it will all work out just fine.
I would have thought that all student pilots should be getting training like this, but unfortunately I know that many are not....
Back on topic - I check for active ASI. I have had an issue in past with a dragging brake so a mental check that acceleration feels normal and no abnormal pull to either side confirms that issue is not present.