Bad, poor, wrong are comparable when they mean not measuring up to a standard of what is satisfactory.
Bad implies a failure to meet one’s approval; it need not imply positive condemnation, but it always suggests that the thing so described falls below the mark or is not up to what one would call good.
It often also implies positive harmfulness. Sometimes it suggests corruption or pollution.
Often also it may suggest unpleasantness in any degree, in this sense ranging from the merely displeasing to the strongly offensive or painful or distressing.
Poor also implies a failure to reach a satisfactory point or level, but it usually imputes to the thing so described a deficiency in amount or in returns or a lack of a quality or qualities essential to excellence; thus, apoor crop is one that is relatively scanty; poor land is wanting in fertility, while bad land lacks the potentiality for agricultural development; a poor book may be devoid of interest or artistic quality, but a bad book is commonly offensive to one’s sense of propriety; a poor carpenter is one lacking in skill.
Wrong (see also FALSE) implies a failure to conform to a strict standard; it suggests deviation from a standard of what is satisfactory or, more specifically, fit, appropriate, proper, or orderly.