Martin Van Creveld gives some analysis in The Age of Airpower.

Developed by the army, the [V-2] was a magnificient technical acheivement but owing to its inaccuracy and the relatively small warhead it carried, it never justified the vast resources invested in it. (page 117)

Starting in September 1944, about 3,000 of the missiles were launched at targets in Western Europe and Britain. Since they traveled at several times the speed of sound--the noise of their arrival actually came after they had hit their targets--there was no advance warning whatsoever. The only way to defend against them was by bombing the launching sites...Fortunately for the Allies, the missiles were none too reliable so that quite a few of them never even came close to performing as planned. Gyroscopically guided, they were also extremely inaccurate. On the average, each launch only led to less than one person being killed. Indeed it is estimated that the number of slave laborers who died building the was far greater than the number of people actually killed by the missiles. The impact on Allied morale was considerable, but one can only concur with the historian who argues that, considered in terms of cost/benefit, they represented an extremely wasteful effort. (page 216-217)

Basically, the V-2 was a revolutionary weapon, and it clearly had some advantages that were utilized in future missiles. Improvements in range and accuracy were needed to make it a worthwhile weapon. Somewhat obviously, though, an unmanned rocket risks no pilot or aircrew, so the risk to German personnel was slight. The another glaring defect in the V-2 was its limited warhead, as even when it was able to hit its target it was unable to cause widespread destruction. This development would only come with the pairing of nuclear weapons with long-range missiles. So, in response to your two questions--

1: The V-2 was inaccurate. Bombers had the potential to be more accurate, especially in daytime raids. These were extremely costly, and nighttime bombing accuracy was a difficult proposition. Various methods of navigation were used, especially radio beams, but even these relatively inaccurate methods were much more accurate than the V-2.

2: As seen in the quotes, the V-2 was not a cost-effective weapon. Bombing cost Germany more manpower, as there was little risked in V-2 attacks.

As for the psychological question, that was the disturbingly new thing from the V-2. The warhead--when it did manage to find its target--would arrive with no warning. V-1's could be intercepted, and German bombers were eventually violently dissuaded from making the attempt to bomb Britain. The V-2, however, had to be assaulted at its launch site. As such, many Allied bombing raids were diverted to attack them, and ground forces were eventually needed to overrun the launch areas. While damage to the military was slight, the Allies had to devote a good deal of resources to eliminating the threat of supersonic warheads raining down (however inaccurately) on the British Isles.