Inconsistencies
One inconsistency within the series is the method of energy production on Earth. In I, Robot, the main method is stated to be solar space stations, which are apparently obsolete by the time of the interview with Susan Calvin. In The Caves of Steel, the main power source is uranium nuclear stations, while solar space stations are stated to involve engineering problems which are still unsolved. According to Robots and Empire, uranium has fallen out of use a very long time ago and is all but forgotten, fusion based nuclear reactors aren't used on large scale, and nearly all the power comes from solar space stations.
Another inconsistency is the positronic brain development. In I, Robot, by the end of the book, there are "Machines", brains of power sufficient to calculate human actions and give recommendation on global scale, and a humanoid robot is stated to be indistinguishable from a human being by any external examination, even by a high quality robopsychologist. In the Elijah Baley series, however, no positronic brains of such power appear to exist, and a humanoid robot is rather easily distinguishable from a human being if the difference is looked for specifically.
In The Naked Sun, a major plot point is that R. Daneel is able to masquerade, on the planet Solaria, as a human Auroran and goes unrecognized by both robots and Solarian humans as a humaniform robot. In the sequel, The Robots of Dawn, however, Elijah Bailey and Daneel have a detailed discussion about the fact that NO Spacer, including non-Aurorans, would ever confuse even a humaniform robot like Daneel for a real human being due to the mechanical behavior and mannerisms of a robot. However, it's worth noting that Solarians are significantly different than other Spacers in many ways, and that they have "unusually rigid mental attitudes toward robots."
Read more about this topic: Robot Series (Asimov)