There are two main reasons a telescope doesn't track perfectly: polar alignment error (which you can correct) and irregularities in its mechanism (which you cannot). A third factor is atmospheric refraction: objects very close to the horizon appear slightly higher in the sky than they ought to, and the extent of the effect depends on humidity, so it's not completely predictable.
Mechanical tracking errors can be periodic or random. In real life, you get a combination of the two. Periodic errors recur with every revolution of a gear -typically once every 4 or 8 minutes - and some computerized telescopes can memorize a set of corrections and play it back every time the gear turns. This is known as periodic-error correction (PEC) and you have to "train" it by putting in the corrections, by hand or with an autoguider; the latter is preferable. On the Meade LX200, the PEC retains its training when turned off, and you can retrain it by averaging the new corrections with the existing set, hopefully ending up with something smoother than either one would be by itself.
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