I film most projects 720P / 50 here in PAL land.

I set the shutter to 180 degrees.

I have not had anything but very good results up until a week or so ago when trying to film a scolling red led sign at a wedding which did captured only half the hight of the sign. I temporarilly turned the shutter on and I was able to capture the sign normally.

What is happening? Should I film with the shutter on or off?

Shooting progressive you normally keep the shutter on.

Switching it off can result in smearing or blurring over any action. However, people do sometimes switch it off in low light situations, but any action can have the blurred artefact and a judgement needs to made if this is acceptable for the content.

By the way... the blur seen on Public Enemies (Michael Mann) was consequence of a 360º shutter angle (off), right?

If you're shooting 50 f.p.s your shutter should really be off for normal shooting. If it's slowmo then the shutter would help with defining edges.
The shutter dictates how long you gather light for. So at 180 degrees and 50 f.p.s you're only gathering light for 1/100th of a second per frame. Good for reducing motion blur, but not good for exposure under limited lighting conditions.
I'd use a 180 degree shutter for 23.976/25/30 progressive shooting and off for higher rates unless it's for effect.

I film most projects 720P / 50 here in PAL land.

I set the shutter to 180 degrees.

I have not had anything but very good results up until a week or so ago when trying to film a scolling red led sign at a wedding which did captured only half the hight of the sign. I temporarilly turned the shutter on and I was able to capture the sign normally.

What is happening? Should I film with the shutter on or off?

The LED display, like a CRT TV screen, isn't actually constantly lit, but is flickering on and off very fast. As with a TV screen you'll need to adjust the shutter speed to get the best results. It's nothing to worry about really.

Personally in progressive mode I only ever shoot with the shutter off if the light is really low and the action isn't fast moving. Otherwise motion blur becomes unacceptable.

And just a bugbear of mine, but I'll get it off my chest. We're video professionals here, we don't "film". For me at least, "film" implies the use of a different medium and a different discipline which is out of the remit of this website. I know this is something that has crept into the popular media with terms like "Jo Blogs filmed this footage on his mobile phone" but as professionals we should at least try and make the effort.

Thanks guys.

So for normal acqusition. Should I use 1/60 sec shutter speed with 720P/50?

As a PAL shooter myself, here's a sort of rough rule of thumb:

Normally, I shoot 1/50th when at 25p.

If I am shooting a computer screen, or LCD/Plasma showing computer info, I shoot at 1/60th, you can see the screen stop strobing.

If I am wide open at the slowest shutter speed and I really need the extra bit of help, I will switch the shutter off, and sometimes this coincides with situations with lots of flash photography, and quite frankly I prefer the results of 'no shutter' in flashy situations. But you must make your own tests and decide.

'No Shutter' is very smeary and adds a sort of dreamy effect to things, the opposite of a fast shutter adding a jittery sports/action feel to things.

In a perfect world, one would add more lights or ND to shoot at your required aperture at 1/50th (25p), 1/60th or thereabouts (29.97p), or 1/48th (24p), but there are times when you do what you have to do to make it work (and on two shoots very recently, it came to that point where I switch on Full Auto when things hit the fan).

And just a bugbear of mine, but I'll get it off my chest. We're video professionals here, we don't "film". For me at least, "film" implies the use of a different medium and a different discipline

Well, we don't actually video either, in the sense that video is historically tied to tape. And many film makers don't film, as they're shooting digital. So it's really a bit of a mess. Some might argue that we really need a new term, to properly represent the technology in use. I thought that for a while, but I don't anymore. "Film" or "filming" or "film making" aren't terms that are for most people, necessarily wedded any longer to celluloid. They are rather, terms that suggest working with moving image sequences, without regard for the specific technological source of the images themselves. In that sense the terms, though lacking rigid precision, generally work just fine.