Our production Oracle Database version is 10g. I am trying to install either 11g or 12c on my local machine primarily to access sqlldr. I am wondering if there are any compatible issues.
Metalink has the definitive client/ server compatibility matrix. It will depend on the full version of the target database. Assuming "10g" means 10.2.0.2 or later, you should be fine with a 12.1 client. If the database is running something earlier than that, you'd generally need an earlier version of the client to be safe.