Short answers, pulled from the story.
Observational error, also called measurement error, is the difference between a measured value of a quantity and its unknown true value. Such errors are inherent in the measurement process itself and are characterized in terms of two components: random error and systematic error.
Random error produces inconsistent results that scatter around a true value and can be reduced by averaging repeated measurements. Systematic error always acts in the same direction and cannot be eliminated by repetition; it stems from causes such as imperfect calibration, environmental interference, or flawed methods of observation.
A stopwatch that begins with one second already on the clock introduces a zero error: every timing taken with it will be off by one second, regardless of how many times the experiment is repeated. A metallic ruler whose temperature is uncontrolled is another example, as thermal expansion introduces a systematic inaccuracy into every length reading.
Precision refers to how closely repeated measurements agree with each other, while accuracy refers to how close those measurements are to the true value. An instrument can be precise but inaccurate if a systematic error shifts all its readings consistently away from reality.
Constant systematic errors can only be detected by checking an instrument against an independent known standard. A spectrometer, for example, can be verified by measuring the D-lines of the sodium electromagnetic spectrum at 600 nm and 589.6 nm. Calibration of the measurement instrument is the common method to remove systematic error once it is identified.
Attenuation bias occurs when one or more independent variables in a regression model are measured with error. In that situation, the regression coefficients and standard hypothesis tests become invalid. When only the dependent variable carries measurement error, the coefficients remain valid but the R-squared value is lower than it would be with perfect measurement.