There are a few obvious factors to being able to detect resolution differences: the resolution of the screen, the size of the screen, and the viewing distance. To be able to detect differences between resolutions, the screen must be large enough and you must sit close enough. So the question becomes "How do I know if need a higher resolution or not?". Here is your answer.
Based on the resolving ability of the human eye (with 20/20 vision it is possible to resolve 1/60th of a degree of an arc), it is possible to estimate when the differences between resolutions will become apparent. Using the Home Theater Calculator spreadsheet as a base, I created a chart showing, for any given screen size, how close you need to sit to be able to detect some or all of the benefits of a higher resolution screen. (Click the picture below for a larger version.)
