As said, run-of-the mill errors are a bit of a black eye, but no, there’s not really any formal penalty. Some, maybe even most, may not even rise to the level of black eye and just be areas where “reasonable minds may differ.” I even saw one reported opinion where a U.S. District Judge in Dallas made note that the Fifth Circuit Court of Appeals reversed him the last time he made a ruling in a case similar to the one before him, but said he was making the same ruling nonetheless. Basically he was saying “I was reversed last time I ruled this way, but I’m doing it again beacause you appellate court jackasses are applying the law incorrectly.” It was that delightful mixture of learned and crotchety that only lifetime tenure brings about.
Somewhat more surprising is judicial immunity from personal suit that can apply even in cases of serious and intentional wrongdoing. In the case of Stump v. Sparkman, 435 U.S. 349 (1978), a judge allowed the sterilization of a slightly retarded 15 year old girl in an ex parte proceeding with no hearing, no notice, and no attorney ad litem. The girl did not even realize she had been sterilized after the operation was complete; she was told that she was having her appendix removed. The Supreme Court ruled that he was immune from damages for deprivation of civil right even if he was acting in error, maliciously, or in excess of his authority, so long as he was arguably acting within his jurisdiction. That’s a very, very extreme example, but it gives you the idea of how far judicial immunity can reach.
On the other hand, I assume a judge can be held in contempt for refusing to abide by a writ of mandamus, but I don’t know any judges that crazy.