Nokia Lumia 820 - Why am I unable to see the app update notification on Windows Phone Store tile?

There is a brief period of 24-48 hours while your app updates show up as a number on the Store Tile. The Store check for update is run once for every 24 hours. Note that if a data connection is not available, the update will not run again for 24 hours. Try the following: 

1. Make sure that you have date and time set correctly on your phone (Settings > date+time).

2. Check your internet connection: Open the web browser and check if you can access to Store by entering the address in your browser address field.

3. Tap and hold the Store tile, and tap unpin icon. Then go to the application list and re-pin the Store app to the start screen.

4. Make sure that you have authorised Microsoft to send messages to your number for Store notifications. Use a desktop browser, sign in to your Windows Phone account using the phone's primary Microsoft (Live) account ID, and then select Update on the left side.

5. Turn off at least one app with background tasks enabled (the app update notification may not be shown if the background tasks exceed a certain limit (around 15).

  1. On the start screen, swipe left, and select Settings.
  2. From the settings swipe left to applications tab, and select background tasks.
  3. Tap on the installed app you want to modify, and then select block.
  4. Tap the Back key to return to the start screen.
  5. Unpin the app from the start screen.