Plot holes: There are several apparent violations of various of the three laws of robotics, some of which can be resolved by careful reasoning, some of which cannot. All the violations serve the drama and only bother you if you think about them too much. So don't.
Continuity: Level of beer in glass when Rupert is telling Andrew about being able to taste.
Continuity: When Andrew is walking through the park with Portia, his shirt is wide open. When they stop to talk, it is almost closed. When they walk again, it is open again.
Factual errors: Some of the continents on the world map in the council chamber are in the wrong positions, notably South America (which is rotated significantly) and Australia (which is directly below India). This may have been an attempt to illustrate continental drift, however, these continents would not have moved that significantly in only 200 years.
Continuity: When Andrew and Portia are playing chess in the park, the chess board is at first very unusually set up as most of Portia's pieces are on the board side closer to Andrew and vice versa. In the next moment, the board has changed completely.
Errors made by characters (possibly deliberate errors by the filmmakers): At the end when Andrew dies and Galatea, the nurse, is checking up on him, you can clearly see that his chest is still moving up and down as if he was still breathing even though he passed away a few seconds earlier.