Developer menu available in Safari? If so, go there and under the third menu item, the name of your machine, see if Automatically Show Web Inspector is on.
Long shot, as this flags does not seem to do this, but, from a Terminal, run the following as see if WebInspectorAttached is zero. I toggled it and did not seem to cause the inspector to always open.
Code:
% defaults read com.apple.Safari | grep WebKitInspectorAttached
WebKitInspectorAttached = 0;
WebKitInspectorAttachedViewHeight = 0;
%