If you have cleaned up the wire you are talking about and it seems full size and doesn't have any issues like the connector connections (ie wont pull out when tugged), then you have done enough.
You can better ground your system as people have indicated, but that is up to you as a further enhancement.
Your alternator that you tested and took back had a voltage regulator problem, as it was overcharging and it should have turned you alternator light on while it was at 15 or higher.
The voltage regulator is an electronic part and has a "high infant mortality" situation, where if it is going to fail, it will do it fairly soon after the install.
The whole alternator gets quite hot when in service, if you need proof, try to remove one right after it has been running.... I will guarantee you will have to wait for the cool down period.