There are many factors influencing sharpness and perceived sharpness. Without any concrete example it is hard to give a precise answer, but you might want to consider looking at Why are my photos not crisp? and Why am I having trouble getting sharp results with my new DSLR, compared to a point and shoot? in order to eliminate some of the most common factors.
Note that the lens gets very good reviews at http://kenrockwell.com/nikon/5018daf.htm and http://www.slrgear.com/reviews/showproduct.php/product/97 in particular regarding sharpness, but keep in mind that the Nikkor 50mm f/1.8D is probably not very sharp at f/1.8 (especially off the center) giving the image an overall soft look. At f/1.8 you also have a very narrow depth of field, thus making it hard to get the focus right (see also Will using a lens at max aperture ("wide open") result in poor images? and Is it difficult to focus on 1.4F prime lens, and if it is how to counter that? ). So, try stopping the lens down to at least f/2.8 or even more (look, e.g., at the sample pictures in the links above which are at f/8). Note that if using maximum aperture is the cause of your problem, then buying an even more expensive lens (which would probably be a 50mm f/1.4) might even make the problem worse.
There might be several reasons why you seem to get more "keepers" from your kit lens. One of them might be that the kit lens's widest aperture is around f/3.5, giving it a wider depth of field and thus making it easier to hide focus mistakes (see links above). Another reason might simply be that you have more experience and practice with the kit lens.
One simple experiment you might want to do is taking pictures of the same scene at, e.g., f/1.8, f/2.8, f/4, and f/8 and compare them. Also, after taking pictures, use your camera's display in order to check whether focus is really where you intended it to be (zooming in to the part that you focused on), and you should see that at in particular at f/1.8 this might not always be the case. Finally, try to get as much practice as you can with your lens, in particular in situations where there is enough time to carefully compose, check settings and results, and retake pictures if necessary. This will give you a better feel for the lens and help you deal with situations where there's more rushing necessary.