Figured it out as soon as I posted this. The problem was profile switching in G Hub. Apparently there's lag in the G Hub profile switching tgat prevents the mouselook from taking on the first click. Setting the SWTOR profile to persistent in G Hub caused the behavior to go back to how it was with Logitech Gaming Software.

I recently upgraded from a Logitech G700 mouse (which uses Logitech Gaming Software) to a Logitech G604 mouse (which uses G Hub) and the behavior of the mouse has changed. With the G700 mouse when I ran SWTOR in Fullscreen Windowed mode, if the game didn't have focus, and I right-clicked in the game window, the game window would immediately get focus and I would be able to mouselook immediately. With the G604 mouse now the behavior is, if the game doesn't have focus and I right-click in the game to mouselook, it won't mouselook or it just mouselooks for like a tenth of a second then stops (the cursor just moves around but the camera doesn't pan). I have to right-click again in the game window for the mouselook to work. Anyone else seen this behavior and found a fix/workaround?

I literally just made this connection today after having done Voss on Imp and Pub many times before. Glad someone else figured it out sooner. Definitely not a coincidence.

FYI you now need to be minimum level 60 to pick up the starting mission from Galen Besk.

Sent both COD

Seconded

This sound is caused by Windows trapping the Alt key, because Windows reserves the Alt key for use in menu selection. Since SWTOR has no menus, it produces the Default Beep that others have mentioned. Unfortunately there is no way to tell Windows not to trap the Alt key. One way to resolve this would be for SWTOR developers to modify their code such that the SWTOR game client contains a hidden menu that allows Windows to correctly trap Alt but do nothing, hence no beep. Many games do this, which is why most people haven't seen this problem in other games (for example, LOTRO doesn't beep, but AOC does). For more code-geeky information on this topic, check out this link: http://chrisprogrammingtips.wordpress.com/category/annoying-windows-beep-on-alt-key/