The federal law would vary between appellate court circuits as the different courts in some cases come to different rulings, with no higher court to reconcile them. In some cases, that might force Congress to pass additional legislation. So it would be difficult and inconvenient, but hardly the apocalypse.
I think the bigger problem would be that there would be no federal check on state Supreme Court decisions. That's kind of a problem if you're hoping to protect constitutional rights.
Good point. But the real problem is not that a state highest court, might get interpreting federal law "wrong" (just like an appellate court), but if the appellate court circuit covering a state goes one way, and the highest state court goes the other way. Then the law is different depending on whether a case goes to state or federal court. Plaintiffs in cases with both state and federal issues would have an advantage, since they would get to pick where to file. If there is only federal issues, the defendant would remove to federal court, and thus the appellate court holding would prevail. So plaintiffs would have a huge incentive if they would win in state court, to find some state issue to litigate along with the federal one.
