According to the caption on this video, the two witnesses were standing on the promenade of Armon Hantziv in Jerusalem when they saw a bright light in the sky at about 01h00 in the morning. They started filming and were in time to capture the light descending rapidly to hover very close to the ground, directly over the Dome of the Rock in the Jerusalem old city, a site of religious importance. After hovering for a while, the light then shoots up extremely fast and vanishes into the night sky, leaving only a blinking pattern of much dimmer lights.
It's all very impressive but there are a number of reasons to believe that this is a hoax. Firstly (and this is probably the weakest argument), the two witnesses don't seem particularly surprised by what they see. They respond like spectators at a fireworks show, oo-ing and aa-ing and WOA-ing at the right times, but there's no sense of mystery, of "What on earth is that?". Still, I'll concede that I'm no psychologists and since I don't speak Hebrew (I assume that's what they're speaking?), I can't really gauge their responses.
The second problem I have with this clip is this: Israel is not a complacent, peaceful country. They are a small nation surrounded by enemies. Neighbouring countries have attacked them in three different wars since the 1960's, they are permanently involved in violent armed conflict with Palestine, and sound distinctly nervous about which direction Egypt may lean when its current troubles are resolved. There is no way a mystery aircraft could get away with swooping around over such a culturally significant city without some sort of military response. UFO nuts might insist that their amazing technology makes them invisible to radar, but the UFO is still quite plainly visible to the eye, shining very brightly. No, the odds of only a handful of people seeing anything, and all of them having their camera's out and ready to film are pretty slim. The video should have shown anti-aircraft guns blazing, fighter planes intercepting, some sort of response from the general public.
Then there are the basic physics issues. When the UFO suddenly shoots up at the 0:55 mark in the video, it accelerates extremely violently. It's hard to judge speeds when we have no frame of reference to determine how large the object is, or how far away it is, but the rate at which it vanishes from the frame suggests it's moving many times faster than sound. My rough back-of-envelope calculations suggest an acceleration on the order of 400G's - enough to reduce any pilot to a bloody pulp on the floor beneath his chair. And there should have been a sonic boom. Since it's practically at ground level, the newspapers the following morning should have been full of reports of a mysterious explosion which shattered windows all around the old city. Then there's the sudden flair of light before it takes off - anybody who's ever handled a video camera at night when there are bright lights will have seen how the frame either flares bright from overexposure, or compensates leaving everything else black. Even the human eye does this (which is why astronomers get so tetchy about light pollution at their star parties!), and no artificial camera has yet matched the dynamic range of the human eye.
All of this strongly suggests that the footage is faked. Which brings us neatly to this video clip, produced by somebody who's done a bit of video editing and visual effects.
Jerusalem UFO - how it was made
The sound is a bit soft on this one, so I'll summarise what's going on. The excerpt from a training video shows how to create artificial "camera shake", to make it look like the footage was filmed on a hand-held camera. Having created the shake, they show how this results in blank areas on the borders being created by having the image move out of the frame. They solve this problem by extending the edges of the frame, using a mirror image of the original footage. You can see how this works quite well, provided the magnitude of the shaking isn't too extreme. But when they analyse the UFO footage, you can clearly see the mirroring effect in action. Go back and watch the original clip at the top of the page, and see for yourself that the mirroring is still there.
What does this tell us? The original footage was digitally edited to make it look like it was filmed on a hand-held camera, which tells us that the original recording was not shaky at all. Although this does not conclusively prove anything, it does strongly suggest that the camera was mounted steadily on a tripod, which in turn implies that the shot was all set up before hand. This recording was not created spontaneously, but planned in advance (which also would explain the nice composition of the picture with the sky framed by the city and the tree).
I should mention that, although it was not obvious to me how the shot was faked (Various other people already worked it out, I just read their commentary), it was obvious that the shot COULD be faked. This is the age of digital photography, Photoshop, computer graphics and digital video editing. We really shouldn't ever be convinced by a picture or video of anything. If I claim something amazing has happened, a picture or even a video is simply not valid proof. It's just too easy to fake.
Correction: In a previous draft of this document, I incorrectly stated that Jerusalem was the capital of Israel. Thanks to reader José Donneys for pointing out that the capital is in fact Tel Aviv.