The 580EX should be fired in perfect sync with the 7D. Definitely when below sync speed. You seem to have a lag in your system here so the flash fires a fraction of a second after the 2nd curtain starts to close.

UPDATE - just noticed that the flash is actually mounted on the light stand and shoots through the umbrella - and it looks like you are using a non TTL wireless trigger to fire the flash. In this case it is possible that the radio trigger introduces that lag.

UPDATE 2: You can try setting the trigger to 1st curtain if it is set to 2nd curtain and it may help overcoming this lag with the slower shutter speed (say, 1/160).

I wonder why you don't use the built in remote flash controller in the 7D? The 580EXII+7D are a (almost*) perfect match in this sense.

(*) almost, b/c it does not support high-speed sync (HSS) mode in wireless mode.

UPDATE 3: from the new images you posted and the new description, it seems like you tried to trigger the flash through the radio trigger while it was also set as a wireless Master. I think it is not really designed to be a master when you trigger it by the simple trigger, and it may fool the flash. Another possibility is that when it receives the trigger signal it first transmits its control signals to (what it thinks to be) its slaves (which do not really exist). This causes the lag!

To sum-up, the 580EXII is supposed to work as a Master (to control remote slave flashes) ONLY when connected to the hot shoe - that is, directly mounted there or connected with an ETTL cable. Otherwise, it can be an ETTL optical slave (if you have the Canon ST-E2 controller or another 580EX as a master), or a full manual, non-ETTL slave, triggered with the simple trigger signal (like what the Cactus transmits or a PC-Sync cable will allow). Your last piece of information probably confirms this.