The Dome of the rock is closed to non Muslims, but infidels are occasionally allowed to walk through the outer courtyard. There is clearly a lot of tension about allowing even this. When I did my visit we were required to walk directly from the courtyard entrance to the nearest exit. We were not allowed more than a few feet from the outer wall and were required to keep walking. Anyone who stopped to take a photo got shouted at.
The Muslims inside didn't seem pleased to see us. Several people shouted things about Palestine at us and one guy, who seemed to be medically as well as religiously insane was swinging his arms around in a threatening manner. Not a nice place.
Next up was the Church of the Holy Sepulchre - the site where Jesus may have been buried. I had been here before, but I thought it might be more interesting on a Sunday. It was indeed. The church is divided into a religious food court with many different sub-chapels each controlled by different religious sects. When I visited, several of them were trying to have services simultaneously and it felt like a rap battle.
The final stop of the day was the Dead Sea. I took a bus there and ended up partially hitchhiking back because I missed the proper bus. The Dead Sea was roughly as a expected. When I lie back I'm almost lying on top of the water rather than in it. Standing up is quite hard because your legs are so buoyant. If you try to stand up then your legs will want to lift up and you are likely to end up falling onto your face. Another interesting effect is that the water feels kind of slimy and leaves a slippery film on your body. The water also feels thicker than normal water.