If you are performing numerical computations, then a more likely source of error is in roundoff or over/underflow. In these cases, I wouldn't say that the CAS is necessarily in the wrong, just that you need to know the properties of the underlying algorithm and either recast your input or reimplement it in a more numerically robust way. In such cases, decent introductions to numerical analysis should give you a feel for the types of issues you need to worry about.
Of course, on the matter of symbolics, then there are no excuses for errors.
