There is this part of my map where I keep falling though the ground. I have used different textures for that part of the map, but I keep falling through.

are you sure that part of the map isnt a _blend texture? actually not positive if you can fall threw those but you can see threw them and it looks funky. is it a custom texture? maybe the you could of done something wrong in assman. did you accidently select a brush and make it noncollidable in radiant? these are all questions you should be asking your self to begin with and i hope you have checked this already. if none of those could be the problem could you take a picture of the texture in radiant?

I have the same problem, just in my case in radiant I cant see the texture, but when compiled it's there it can be seen and fall through it.
In radiant I can't see it or select it to delete it.

maybe hidden or on a different (disabled) layer in radiant?

there's a menu entry to reveal hidden geometry back again, and layer visibility can be set in Layer window (L key)

but sometimes Radiant f**ks up and creates bad geometry, which can't be selected. I think drawing a brush around it and select inside works, just not Shift + Click