Okay...can somebody out there give me a straight answer... what ARE Star Trek sensors? is it radar? I'm assuming that's obsolete... but what is it? how does it scan?
I would think starships use different kinds of sensors for long- and short-range.
For nearby objects, they could very well use light- or graviton-based sensors like radar, which would send out a light pulse and then measure the reflection off nearby objects. They could also use passive sensors, which simply detect incoming radiation, such as light, ultraviolet, infrared, X-rays, nutrinos, gravitons, etc.
However, this method is not effective for long-range scanning, since some objects move faster than light. For example, if you try to detect another starship that is one light-year away, it would take the radar beam one year to reach it, and another year for the reflection to return. So you wouldn't know about the other starship for two years, even though they could go to warp and be right in front of you in a few hours.
An example of this shortcoming of short-range sensors was seen in the movie "Star Trek Generations," when the Enterprise-D crew saw the nearby star explode through the ship's windows without any prior warning. (The star was several light-minutes away, so it exploded several minutes before the flash of light reached the windows of the ship.)
Another example is in the TNG episode "The Battle," where the Picard Maneuver was used to confuse another ship's sensors, by jumping to warp to another nearby location while the light reflected from its previous position is still reaching the other ship, making it appear to light-based sensors that the ship is in two places at once. (You'd think after all these major screw-ups over so many years, that starships would stop using light-based sensors.)
A more effective sensor technology is subspace-based, which can detect distant objects and ships faster than light -- almost instantaneously. For example, if a starship is one light-year away, the crew would detect it immediately using subspace sensors (rather than two years later using radar), and if a star explodes five light-minutes away, the subspace sensors would detect it immediately, five minutes before the light from the explosion reaches the starship's windows.