I saw the picture you posted of the castle this morning on the "image below me" thread. Your shutter speed was 1/60" which is getting pretty slow. You need to try and make sure the camera is stabilized -- either on a tripod, resting on a fence, or just try holding your breath and staying as still as possible while taking the photo. That would help with motion blur.
I don't think there's motion blur in that photo though. It looks to me like it's not in focus. Another thing is that your flash fired. That would light up the foreground, like that person's head on the right side of the photo and the other people in the foreground, but the background would be darker. That's okay if you're trying to shoot a portrait at night, but if you're just trying to take one of the castle, you didn't need flash.
If you increase the ISO, you also increase sensitivity to light. That can help keep exposure times shorter (= less blur) but also introduces noise into the photo. In your shot of the castle, your ISO was 160. Newer cameras have higher ISO capabilities which help with lower light settings.
I was there the same time you were! We had a fantastic time but I was glad to be leaving when we did. The crowds the last couple of days we were there were getting crazy! The 20th was our last night there and I was walking around taking photos while DD9 and DH were at Space Mountain. At about the same time you took the photo of the castle I took this one from the train station:
The book that Gianna's Papa recommends is also an excellent read for getting a grasp on the fundamentals of photography. A DSLR in auto mode will get you better pictures, but to really get the most out of any camera, even a P&S, it's best to understand what is going on in the camera and how to use the settings to get the image you want.
On this trip I didn't take my DSLR, but only my mirrorless camera, the Olympus E-PL2. It has the same sensor as my DSLR, but in a much smaller body. The photo above was taken handheld at 1/13" (I was standing REAL still and had image stabilization turned on) and the ISO was 1600.
Good luck!