iTerm2 does not take the focus with the hotkey window
This one had me too. Just untick "Floating window" and restart iTerm2.

Full directions:


MENU: iterm2
MENU ITEM: Preferences...
TAB: Profiles
LIST ITEM: [Your Hotkey Profile Name]
TAB: Keys
BUTTON: Configure Hotkey Window
CHECKBOX: Floating Window &lt;= UNCHECK THIS