My Own Worst Enemy/WMG

It's all The Plan by Edward.
We know that he's been keeping secrets from the agency ("We only found out about this place last year") and we know he's good at being sneaky (how he disposed of the baddie in the pilot), what else is he hiding/planning?

It's all The Plan by Henry.
He's the one manipulating events, while appearing to be a confused bystander.

The glitch in the Edward/Henry switch was caused by the computer tech's misuse of the mainframe.
First of all, you don't hook up your secret supercomputer to the internet. Second of all, you don't install or play World of Warcraft on it.
 * The glitch was caused by a virus (or a WoW-related computer bug), or by a deliberate hacking attempt.
 * He's just lucky Henry didn't charge at the mob boss shouting Leeroy Jenkins!

Henry is the real personality.
If you employ a brilliant super-spy, it's hard to understand how transforming him into an average suburban businessman helps you. But brilliant super-spies can't be that common. So if you could transform someone into a brilliant super-spy, it would be worth it. Even if the technique works on so few people that you have to use an average suburban businessman as your subject.

Neither is the real personality
There is a third, as of yet unrevealed personality, who is the original. The other two are artifical and dominant.
 * Edward just thinks he's the original.
 * Or, that's what he pretends.
 * The real one is the running The Plan.
 * Christian Slater is the real personality.

Tom/Raymond is not being switched
Tom is simply a regular agent with a regular cover identity.
 * He doesn't display any of the dizziness and disorientation that accompanies Christian Slater's switch.
 * He mixes elements of both lives, when he calls to reassure his wife during a mission.
 * And he was just being a dick when he was pretending that he had two personalities.

Raymond has a rivalry/dislike of Edward
Hence Raymond's amusment with making casual threats to Henry.
 * Henry and Tom are coworkers and friends. Edward and Raymond are coworkers and enemies. It fits with the whole theme of inversion.

We haven't seen the last of that Russian guy
'Dying' would take him off the radar.
 * And restore the Boss' confidence in Edward. Edward was behind it all!
 * And clearly a case of Foe Yay.

Henry is the real evil side.
He's a lot better at acting normal than Edward, and is waiting for the day Edward loses his usefulness so that they can permanently suppress Edward and completely forget about them. Then his day will come. His day... to rule.