How serious a problem is it for an outlet's ground wire to be extended from an outlet that is part of a different circuit than the circuit providing the power and neutral wires? I have an old fashioned fuse box - if a fuse blows for the circuit associated with the ground wire then does that mean that an outlet connected to that ground wire is no longer grounded even though it will still be getting power since it is associated with a different circuit? That is the one potential problem I can see with this set up but just wondering if this is how it works, and/or if there are other problems associated w this set up. Thanks!!
Before National Electrical Code 2014, this was not allowed. However, if your area has adopted the 2014 version of the code, this is now legal as long as both circuits originate from the same panel (250.130(C)(4)).
See this answer for more detail.