He pointed towards the outside of the room
I'm wondering if that's a grammatically correct sentence. It sounds a bit off, but after analysing it a bit, there doesn't seem to be anything wrong.
He pointed towards the mountains.
That sounds fairly well and there doesn't seem to be any problems. "The mountains" is a location, and "the outside of the room" is also a location, yet the first example sounds slightly wrong for some reason, but I can't see which part is wrong.
Best Answer
As you say, there's nothing actually wrong with the sentence itself. It is grammatically correct.
The reason it sounds 'off' to your ear is that pointing, as an action, is supposed to indicate something with a relative degree of precision, but 'the outside of the room' is an indeterminate location - it includes the shop down the road, the nation of Paraguay, the International Space Station and the constellation of Orion. How do you precisely indicate all that with one finger?
So the sentence doesn't really make sense, and gives little useful information.