See post #36
This applies to air frame breakers as well as molded case types.
We find that most of the time breakers fail to open or close all phases is due to not being operated/ exercised on a regular basis (we recommend a 3 year interval for exercising and current injection.) Add to the fact that breakers are not normally opened up until a problem exists. This is especially true if the breaker is not part of an automatic transfer switch that at least gets operated on a power failure. Over time the grease dries up and mixed with the dirt causes the linkages and mechanism to seize up and not slide easily to latch and close properly. Powering down, removing the cover , cleaning the old grease, re-lubing the mechanism usually corrects the problem, unless of course a part fails that has to be replaced. Think of it as the same as if you did not drive your car for months (years?) and the problems you would encounter.
As to your first question about a breaker tripping (opening on a fault) properly, this is determined during the 3 year PM schedule where thru primary or secondary current injection tests the breaker is evaluated for continued service.
For a good reference see the NETA acceptance and maintenance specs.