And from mine (about a month of owning a 32DX7) i'd say disable the 'Movie Theater' mode too!

I noticed it was causing a small problem where the Sky menu system would ever so slightly corrupt from time to time (looked like a slight delay in the deinterlacing occasionally) - i never saw it cause any problems with anything else, but disabling it didn't seem to make the picture or it's movement any worse either.
I found that 'DigiPure' can help with some picture problems, but has too many little side effects to be left on all the time. 'Colour Management' as i've said has some horrible side effects on a poor picture which seem to bring out the weaknesses in a bad signal leading to colour banding all over the place for a start, i can imagine it improving a really good picture as it definitely made colours more vibrant but in the case of 99% of channels via Sky it just doesn't work. 'Picture Management' and 'Smart Picture' play around with contrast on certain colours and from what experimenting i've done (as standard i always have them set to off) it seems to be a 50/50 case of improving the picture or slightly degrading it, and i'd rather have the consistancy of them being off. 'MPEG Noise Reduction' does seem to help with noisy pictures via Sky, but it's only a subtle difference and so i can never really decide if i should have it on or not (right now i do though, for what it's worth).
So my own advice
Ohanlon, is to turn everything except maybe 'MPEG Noise Reduction' off, and do any tweaking of the picture via the basic backlight/brightness, contrast, sharpness, and colour settings. Find a good picture with the processing off and then by all means go in and compare each picture processing option on and off to decide if you find anything which does actually improve the picture to your own eyes.
To be honest, even going back to when all the big companies had CRT's at the top of their ranges i never once found any picture processing that was genuinely worth having on all the time. As long as the basic unprocessed picture is of a good quality my personal feelings on the matter are that picture processing just introduces more problems than the tv will show up in the original
unprocessed source. With even a half decent source the basic unprocessed picture of the 32DX7 is very good and just doesn't need the extra processing (which is exactly how it should be). The only true way to improve the picture quality without any negative side effects would be for Sky etc., to increase their bitrates, or to feed the tv a HD source.
Of course having said this, people see things in different ways. I'd hate to have a tv where the picture processing couldn't be disabled because i find the more processed the picture is, the more my eyes focus on the processing rather than relaxing and just accepting the picture being displayed. On the other hand i know people who have looked at heavily processed pictures (when i was looking at the old Samsung LCD's just before Xmas instantly springs to mind) and have raved to me about how great the picture looked - to the point where i was beginning to wonder if my eyes were playing tricks on me!

If it looks good to your own eyes that's all that really matters in the end.