How do I capture the point initially tapped in a UIPanGestureRecognizer?

You should be able to use translationInView: to calculate the starting location unless you reset it in between. Get the translation and the current location of touch and use it to find the starting point of the touch.

Late to the party, but I notice that nothing above actually answers the question, and there is in fact a way to do this. You must subclass UIPanGestureRecognizer and include:

#import <UIKit/UIGestureRecognizerSubclass.h>

either in the Objective-C file in which you write the class or in your Swift bridging header. This will allow you to override the touchesBegan:withEvent method as follows:

class SomeCoolPanGestureRecognizer: UIPanGestureRecognizer {
    private var initialTouchLocation: CGPoint!

    override func touchesBegan(touches: Set<UITouch>, withEvent event: UIEvent) {
        super.touchesBegan(touches, withEvent: event)
        initialTouchLocation = touches.first!.locationInView(view)
    }
}

Then your property initialTouchLocation will contain the information you seek. Of course in my example I make the assumption that the first touch in the set of touches is the one of interest, which makes sense if you have a maximumNumberOfTouches of 1. You may want to use more sophistication in finding the touch of interest.

Edit: Swift 5

import UIKit.UIGestureRecognizerSubclass

class InitialPanGestureRecognizer: UIPanGestureRecognizer {
  private var initialTouchLocation: CGPoint!

  override func touchesBegan(_ touches: Set<UITouch>, with event: UIEvent) {
    super.touchesBegan(touches, with: event)
    initialTouchLocation = touches.first!.location(in: view)
  }
}