The problem is passing state around in global variables. Any code can (and readily does) modify the state which is the problem.
You're right that look_ahead/company_address would work as a define("CONSTANT") better but honestly, I hate not putting a $ sign in front of a value (constant or variable). I am more prone to missing a $ than redefining a global. I don't remember ever having the problem of redefining a global unintentionally. I can give 20 examples of when I missed a $ symbol and PHP gave me an error/notice. If PHP constants had a symbol akin to $ (say #), I would definitely use them. But I just feel dirty typing "echo LOOK_AHEAD;" in one place and "echo $look_ahead_partial;" in another because I don't want to get in the habit of putting $ in some places and not putting them in others.
The problem with not using a constant where it's necessary is that you're communicating the wrong thing to someone else or even yourself 6 months down the line. You might want to re-evaluate what you see as "ugly code" especially if it changes how you write the code.
Personally I global the database wrapper, the user session class and config stuff (which yes I could use constants). Although if the code base I'm referring to wasn't 95% me coding I would probably consider using global less.
With "echo $look_ahead" there's no indication of that, and in the future another dev might add something that modifies $look_ahead's value and break other parts of the code, making for sneaky bug (which incidentally is why non-constant globals are so disliked ;))