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I am adressing what looks like an inconsistency.
The invisibility spell says: If a check is required, a stationary invisible creature has a +40 bonus on its Stealth checks. This bonus is reduced to +20 if the creature is moving.
So moving imposes a -20 malus to invisibility.
The "special abilities" mentions "A creature can generally notice the presence of an active invisible creature within 30 feet with a DC 20 Perception check." but the table mentions only a malus of -10 for moving
Invisible creature is... Perception
In combat or speaking –20
Moving at half speed –5
Moving at full speed –10
It seems to me that detecting a moving invisible creature is DC 40-10 = DC30 and not DC20
Armenfrast
France
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There is a discrepancy between the spell and the description of the special ability. I believe the discrepancy comes with the chart (under the special ability) and the "not moving" entry. I believe that entry should be changed to, "Using Stealth, Not Moving," and the value should change to "Stealth +40." That change would reconcile the spell description and the special ability in the following way.
Using Stealth, the creature gets a +40 to its Stealth check because it is invisible. If it is moving while using Stealth, it instead gets a +20 to its Stealth check because it is invisible. The result of the Stealth check determines the DC to notice the creature, as shown on the chart (presuming the chart has the aforementioned correction).
If the creature is not using Stealth, the DC to notice it through Perception is determined by using the first four entries on the chart under special abilities. The base DC is 20, modified by the action or movement the creature is taking.
In either case, add modifiers for distance and obstacles. In either case, to pinpoint the creature's square, add +20 to the DC.
Armenfrast -
It's not that moving imposes -20 penalty, it's that not moving provides a bonus. Base DC plus not moving equals one result. Base DC plus moving equals a variety of results, depending on how fast you're trying to move.
However, you have hit the tip of an Inconsistency Iceberg here, so I'll try to help quickly:
(1) way back in the mists, invisibility was only defined by the spell. The spell gave +20 to hiding, with an additional +20 if you were hiding and not moving.
(2) aeons and editions passed, and the gamegods realised that not all invisible dudes were going to be stealthy. So they introduced an entirely new detection system for invisibility, one that used clean, Stealth-free base DCs. That way, an invisible dude could be stealthy if it wanted, non-stealthy if not.
Unfortunately, the gamegods looked around for a baseline for their clean DCs, and found nothing but the +20/+40 of the invisibility spell. So they adopted those as invisibility's vanilla DCs - DC20 for sense, DC40 for pinpoint.
(3) What made this unfortunate what that they didn't go back and remove the +20/+40 from the spell and the skill listings. So now, if you're invisible and stealthy, you have two 20/40 figures - the base invisbility DCs, and the +20/+40 given by the spell and echoed by Stealth.
This creates some ridiculously high detection DCs.
(4) On top of all this, the Stealth detection system and the invisbility detection system have grown apart with time - and they weren't close to begin with. So now they have a variety of modifiers that don't match. Not moving, half moving, full moving...these are all different for Stealth and for invisibility.
(5) The quick solution: ignore the spell/skill +20/+40. Then bring the Stealth and invisibility mods into line. I've posted a prototype system for it on here, but you can do it yourself once you see what the issues are.
Good luck - it's a big iceberg :)