Is this ground beef safe to eat?
When in doubt, throw it out.

There are three main indicators to spoiled beef:


Texture: beef becomes slimy as it spoils.
Color: beef will go gray as it spoils, BUT, it will also go gray due to it oxidizing. This makes it a somewhat unreliable measure without the other indicators.
Smell: as beef spoils it will start to smell sour. Note that you did mention the smell being sour in your description.


Your beef has hit two out of three boxes. It may just be starting to spoil.
I would consider it potentially unsafe to eat.

But why take the risk?