Problem Sync'ing/Downloading from Google Play
Go to

Settings&gt;Apps&gt;All&gt;Google Play Store&gt;Clear Cache &amp; Clear Data
Settings&gt;Apps&gt;All&gt;Downloads&gt;Clear Cache &amp; Clear Data
Settings&gt;Apps&gt;All&gt;Download Manager&gt;Clear Cache &amp; Clear Data

If you're rooted I would suggest wiping cache &amp; dalvik-cache from your recovery.
Also you could try installing the latest version of google play application using the apk.