Why does the Play Store's download percentage never reach 100%?
This started happening at the same time that Google introduced the concept of "delta" updates.  This means that only the portion of the app that has been modified is sent over, as opposed to the entire app.  However, they never changed how the Play Store app calculates the download percentages - it's still taking app's full size as the base 100%, instead of the size of the delta update being downloaded.  It simply never bothers to check with the download manager (which works correctly, as reflected in the notification tray) for the correct size of the delta.

This is why you are seeing the percentage stop at random times - the difference in sizes of the full app and the delta is what's making the play store think the download is larger than it actually is.  For example, if an app's full size is 10MB, but the update is only 5MB in size, the Play Store will still think it's downloading the full 10MB, and will stop at 50%, when the 5MB download completes.