Line pick woes

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You could always apply the pickmode to all the sub-children using my multipurpose NextChild() function from here:
http://www.blitzbasic.com/codearcs/codearcs.php?code=796
Like this (untested):
level = LoadAnimMesh("E:\blitz3d\mystuff\YOURLEVEL.b3d") 

ent = level
While ent
	If EntityClass(ent)="Mesh" EntityPickMode ent,2
	ent = NextChild(ent)
Wend


Function NextChild(ent)
	If CountChildren(ent)>0
		Return GetChild(ent,1)
	EndIf

	Local foundunused=False
	Local foundent = 0, parent,sibling
	While foundunused=False And ent<>0
		parent = GetParent(ent)
		If parent<>0
			If CountChildren(parent)>1
				If GetChild(parent,CountChildren(parent))<>ent
					For siblingcnt = 1 To CountChildren(parent)
						sibling = GetChild(parent,siblingcnt)
						If sibling=ent
							foundunused = True
							foundent = GetChild(parent,siblingcnt+1)
						EndIf
					Next
				EndIf
			EndIf
		EndIf
		ent = parent
	Wend
	Return foundent
End Function