This decree does not grant military personnel more powers than the police. It just gives them the exact same right. This means they still need a warrant to search your car in absence of probable cause and it means they still need an order from the public prosecutor.
At first glance this just seems like an expansion of the police force, or a simple means of replacing uniforms without having to make new ones, but it’s not. The reason is that military personnel cannot be held accountable when breaking the law. Their testimony cannot be questioned by the general prosecutor. What this really means is that the law circumvents the red tape and allows for legal military authority to bully Egyptian citizens and to stop them from going on strike or protesting. This is in effect a declaration of martial law.
The constitutional annex aims to instil such a right in the constitution, hence giving the decree the legal cover.
In a military organization, laws don’t exist, just military commands. We have seen unlawful murders taking place based on military commands. What’s worse, the military judiciary is so corrupt that it is no judiciary at all. The laws that have been put in place are to meet street protests with violence and to trump up charges against any of the military’s opposition.
The law enforcement decree is enabling a mafia to act with impunity on the streets of Egypt. It is a vital part of the soft military coup that has just taken place.
Update: On Tuesday 26 June there was a court ruling that halted the military judicial arresting authority. The decree was found illegal by an administrative court but remains in the constitutional annex and can be turned into law.
Update II: On December 10, Morsi re-instated military judicial arresting authority until the referendum on December 15.
Update II: On January 28, Morsi re-instated military judicial arresting authority