Well done, Gordon. I don't have this cam, nor likely will I be getting one - but as I do have an early ancestor in the TX1 I am familiar with some of the modes. Just to point out a few things:
1. Re the tripod mount - it seems odd to be off center, however considering the lens is far off to that side, the tripod mount location actually puts it fairly well in line with the lens, nto a bad thing.
2. Re the HDR mode - you noted in your sample that it seemed to compensate the shadows a bit, but did nothing for the blown windows. The way the HDR modes are designed to be used, one needs to meter for the highlights, and the double exposures will take the second shot to expose the shadows and blend the two. If you were metering the room in general with the windows already blown out, the HDR mode wouldn't have done anything at all to them. Just to note for those using the HDR modes - I've had a bit of practice with the DSLR-A550 version, which is absolutely mind-blowing in the ability to stretch dynamic range and expose for ridiculous shadows against bright light.
3. Re the high ISO comparisons - as I believe another thread alluded to - it really is worth mentioning that while on its own, the high ISO performance doesn't hold any advantage over other competition, twilight mode is indeed a feature designed for just that type of use, so to be completely fair in a comparison, the mode should be used and compared to competition. In regular, real world photography, when it comes right down to Joe-Blow on the street...this mode can allow this compact camera to blow competitors out of the water for hand-held low light shots with moderately still subjects. Special feature, yes. But Person A has a Panny or Canon, and wants a hand-held shot of a building at night - they must use high ISO. Person B has the HX5 and wants the same shot...they too can use high ISO and get so-so results like the other shooter, or they can engage Twilight mode and get rather astounding low noise, high detail shots. It takes them no more time or effort to use the mode, so it really needs to be part of any low light comparison with other cameras, to be fair.
I did see your response that you had already returned the camera - just wanted to make that point for those shopping the cam and wondering. With my TX1, I can pull off high ISO results in low light using twilight mode that absolutely destroy anything I've seen from any compact P&S camera, and on par with some of the larger sensor compacts out there. It is a trick feature that all compact cameras really should begin employing.
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses