If you have to say a person dresses well instead of dresses good, then why is it acceptable to say he/she looks good instead of looks well? I realize "looks well" pertains more towards one's health than appearance, but double standards irk me.
"Dress" is a transitive verb. It takes a direct object, as you dress someone or you dress yourself. "Well" is an adverb, which modifies a verb.
If you say someone looks well, using "well" as an adverb, you're saying that the person does a good job looking at things. Well can be an adjective but it usually pertains to health or well being as you mentioned.
"Good" is an adjective, so it modifies a noun. Saying he/she looks good, "good" is describing the person, not the verb "look"