First and foremost, here are definitely lots of other salts. It is brine, after all. You produce a lot of halite (salt), gypsum, calcite, and all kinds of other evaporite minerals.

There are all kinds of things in smaller concentrations, though.

What comes out of a oil/water separator would need lots of additional processing before going to something like an evap pond. It's relatively hazardous stuff for a lot of reasons other than oil (e.g. it can be rather radioactive). It typically goes through quite a bit of additional processing unless it's being immediately reinjected.