I'm watching HBO's The Pacific right now, and it occurs to me that in every movie like this you essentially get two views of the platoon marching--either wideshots of them walking through a clearing or close ups on the face when they walk through forest. But presumably the marines did not only walk through convenient clearings, so how would they march through denser rainforest? And was marching formation a part of military doctrine or would each platoon march as they pleased?
Which episode are you on? I've wondered the same thing; you'll often hear them using terms like "tactical column" and assigning individuals to take "point" or act as "lead scout," but it's not usually really clear what they're doing.
Answering using modern British military knowledge, but:
Firstly what you're referring to as 'marching' in this context would be called patrolling. Marching is the parade ground stuff or (usually) for covering large distances on roads etc.
Patrolling formations are a taught item (as opposed to ad hoc, what the platoon wants as you were suggesting) and to be very contextual. For example in an open field you may move in an extended line or arrowhead formation at 10m spacings during daytime or 5m at night. Along a road you may use a staggered double line (like a zig zag) to cover both sides of the road and allow defence from all sides
In the jungle a tight formation (5m spacings or less are likely) that focuses on area clearing (so a wide formation - think arrow or line again) is likely.
"Taking point" or being "lead scout" simply means you're the guy out front and you call some of the shots (running back to the commander for permission could cost time or lives). It's your job to look out for traps and call a halt if enemies are sighted, for example.
Hope some of this helps.