The logging should be totally disabled now. Sounds like you may still have some apps running the old input manager. It's important to restart all apps after installing the new input manager. Better yet, log out and back in. Please let me know if switching spaces while in a Cocoa app doesn't work. Best,beta4 seems to work fine in Safari, but I too get the Spaces problem. Regardless of which action, it doesn't seem to work unless you're in the main space. In console, no commands are being sent (or at least none are being logged) when in a space other than the primary one.
I've noticed after you perform the one change, the spaces "icon" which graphically shows which space you're in seems to hang (same behavior if you push ctrl+ --> and then continue to hold ctrl down). You have to press a button or move the cursor for it to disappear. Not sure if that implies the action is based on a release of the trigger key, or if it's just that the gestures won't work in a space other than the primary one.
Also, had to set gesture as a global bind, as it wouldn't work when specified for the Spaces app only (this makes sense, but just mentioning for people trying to replicate the problem).
wc