One of the chief problems is repeatability. This refers to the arm returning to the exact same spot, time after time. An analog sensor has known repeatability issues. Suppose a resistive sensor has a 1 percent error tolerance. For analog devices measuring degrees, this is considered accurate. If 1 percent deviation translates into 3.6 degrees of deviation (360 times .01), the arm after positioning may be off by 4 or more inches. The key understanding is that angles are like a slice of a pie. The further away from the point, the wider the divergence, and the wider the error.
All computers and programmable controllers are digital. To convert from an analog output to a digital input, complex circuitry is needed. In the process of converting, part of the signal is lost. The end result is that the controller issues commands based on an incomplete input. The servos, in turn, are controlled by erroneous input. The arm may behave erratically because of the problems converting from analog to digital.
Analog modules are prone to environmental changes. If the humidity is high, the output readings may be slightly different than if the humidity is low. For a robot that has to operate in differing temperatures and humidity, this leads to errors in arm positioning. For an industrial robot, the sensors have to be sealed against dust, corrosive environments and heat.
Analog modules, by and large, are not as durable as digital sensors. They have moving parts, and moving mechanical parts eventually wear out. For this and the other aforementioned reasons, design engineers almost exclusively use digital sensors, or sensors that have no moving parts.