Craft is unable to determine if an update is available at this time No chance to update on my local machine and on my live site.
On the staging site it works but that's the same server as the live site.

I've cleared the caches and checked the logs. 

Local there is only this error:

2016/06/19 19:41:01 [error] [application] Error in Craft\Et::phoneHome. Message: Cannot overwrite an existing license.key file.


But I run the site in DEV Mode. 

Any ideas? I'm a bit unhappy about it :/

Best
David
You're getting that error message because there is an existing craft/config/license.key file in place for your local installation and there is no record of that install on the Craft/web service end.  Likely you've just copied an existing license.key file from another site into this new installation.

So the web service on the Craft end thinks that since it's a new Craft client installation it needs to send down a new license.key file for you to start using.  But the Craft client knows it should never overwrite an existing license.key file, so it reports that error.

Solution: remove the existing license.key file (since it probably belongs to another site anyway) and let the web service generate a new one for you.