Unusual wiring in receptacle connected to switch
Are you sure you rewired this exactly the way you found it?
Any chance you flipped the outlet upside down in the course of swapping it (putting the two wires on the side with the fatter pin, neutral, rather than the shorter pin, hot)?   

Previously, were both receptacles switched, or only one?
Did the old receptacle have the split tab broken off on either side (that bit of brass between the screws)? 

One of the white wires is a switched hot, and that's fine.  Today, that wire Should be marked with tape to show it's not a neutral.  In the past, that was only required if it was not "obvious".

The bare wire can only be the safety ground.  It cannot be used as a conductor in any way, shape or form, so that setup is illegal as heck, and needs to go.   But first you need to understand what the crazy person was trying to do.  The white and bare wires both attached on the neutral side could mean one of two things. 

If you inadvertently flipped the outlet and that was formerly the hot side, and the tab was broken, that would mean he had split the outlet so only one socket was switched, and the other always-hot. And he was supplying those from the switch, through white (OK) and bare (NOPE).  You'll have to look inside the switch to see if he did this.  And if he did, undo it and make it a normal switch loop and have it switch both sockets. 

If those two had previously been conncted to the neutral (taller prong) side, with the tab not broken off, that would suggest he was having problems with the neutral wire, so he bootlegged ground.  Normally nothing damages a cable in a wall, so wire problems are usually at terminations -- so you may be able to fix it.  If the damage is in the cable itself, take the entire cable out of service - a screw which cut neutral may have cut halfway through other conductors, or be touching hot, waiting for a child to find it.