Suppose, in America, a federal Judge is nominated by the President, confirmed by the Senate, and then he/she is wrong a majority of the time: often in the minority if part of a panel, often overruled by an appellate court if the Judge is the only Judge on that bench, produces rulings full of either false premises or invalid logic, etc., etc., etc. ... I know Judges get to keep their positions "on good behavior"; do frequent errors and/or incompetence qualify as "bad behavior"?
The short answer is that federal judges, or rather federal officials of the United States government, can only be impeached for
treason, bribery and other high crimes and misdemeanors as defined in the Constitution. Obviously, incompetence is not included in that list, so the answer to your question would be no.
However, the actual process for impeaching someone is a strictly human process, and the underlying intent of those involved could stem from reasons that might not explicitly fit into the above categories to some observers. So, as with most things, the answer is never that black and white.
Anyone can petition the House of Representatives to initiate impeachment proceedings against a government official, and in fact in the case of federal judges it is usually the Judicial Conference of the United States that first recommends impeachment proceedings based on their ethical and moral standards for their members. The House can then choose to take up a petition (any member can also request their own inquiry) and refer it to the House Rules committee. If the House Rules Committee agrees the petition has merit it is recommended to the House Judiciary Committee and then to the full House. The Senate will then hold the trial and conviction vote should the full House vote to proceed with the charges.
Importantly, there is no requirement that the House prove the charges they are leveling be tied to one of the specific categories laid out in the Constitution (just like there is no law requiring them to cite the article of the Constitution that gives them the authority to pass any law). So, theoretically, they could vote and pass a resolution based strictly on perceived incompetence. However, they would almost certainly phrase it in such a way as to roughly fit one of the predefined categories.
It is also worth noting that this specific issue was addressed by the Founders during the writing of the Constitution. George Mason argued for including incompetence explicitly as an impeachable offence, but was ultimately overruled by James Madison in the final text. So the consideration was made, and the Founders would not approve, but it is theoretically possible.
Mason objected that these grounds were too limited:
"Why is the provision restrained to Treason & bribery only? Treason as defined in the Constitution will not reach many great and dangerous offenses. Hastings is not guilty of Treason. Attempts to subvert the Constitution may not be Treason as above defined-As bills of attainder which have saved the British Constitution are forbidden, it is the more necessary to extend: the power of impeachments."
Mason then moved to add the word "maladministration" to the other two grounds. Maladministration was a term in use in six of the thirteen state constitutions as a ground for impeachment, including Mason's home state of Virginia.
When James Madison objected that "so vague a term will be equivalent to a tenure during pleasure of the Senate," Mason withdrew "maladministration" and substituted "high crimes and misdemeanors agst. the State,"which was adopted eight states to three, apparently with no further debate.1
Generally no, unless the errors are widely acknowledged to be such. Otherwise that would violate the letter and spirit of the Constitution. One man's errors are usually just politics for the other side. But theoretically the House and Senate could all vote to impeach for whatever reason.
Article III of the US Constitution states that federal judges serve for 'good behaviour' (sic).
In Federalist #78, Hamilton said:
The standard of good behavior for the continuance in office of the judicial magistracy, is certainly one of the most valuable of the modern improvements in the practice of government. In a monarchy it is an excellent barrier to the despotism of the prince; in a republic it is a no less excellent barrier to the encroachments and oppressions of the representative body. And it is the best expedient which can be devised in any government, to secure a steady, upright, and impartial administration of the laws.
So the letter and spirit of Article III were to protect against punishing judges for their opinions. Your argument that the judge is making "errors" in an objective sense, but rarely will they be widely admitted as errors. Most people will not notice except when the result is opposite their political preference. So as a practical matter, this is almost always a political dispute.
The legislature has other responses besides removal, such as passing new legislation. The executive can, at least under some constitutional visions, decline to enforce rulings with which he disagrees. Both of these alternatives are less constitutionally explosive and more politically achievable. If a political viewpoint has the 2/3 of the Senate and majority of the House necessary to impeach, then in most cases it could undertake legislative action to obviate the judge's decisions.
However, a movement of politicians with policy-making motives could start a campaign arguing that the judge has some personal flaws requiring he resign or else be removed. Maybe health problems, or insanity or some trend of bizarre behaviors - something suggesting an inability to perform. If enough people accept that argument, then a politically motivated impeachment could be accomplished under the guise of a politically neutral one.
EDIT- Note that this is essentially what happened to Samuel Chase, the only Supreme Court Justice to be impeached. He was impeached for misconduct and bias in judicial actions, but it was highly arguable at the time. The battle over errors is usually subjective.