Confidence levels can be exactly defined if you have a good understanding of the nature of your errors. A systematic error is not a way of expressing an error, but a breed of problem which often plagues experiments. A systematic error biases your measurements in some predictable way, although you may not know how to predict it. Systematic errors can get very complex, but once understood you can modify your results to remove them. A random error is an error which is present every time you take the measurement, but which varies unpredictably in size and direction.
Random errors are always present, but fortunately follow well-behaved statistical rules.
The effects of random errors can be reduced only by repeating the measurement as often as possible. An illegitimate error is not one born out of wedlock, but a one-time mistake in the procedure which produces a bizzare value. Usually the mistake is more subtle, for example misreading a display or an unexpected power surge in the equipment. In this case, people usually use some statistical criteria to throw out data which are well outside the normal range of possibility. The precision of a measurement is the total amount of random error present.