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If the warrant specifically is limited to certain areas of the house and the police then enter other areas that are not listed, anything found there that is seized can be challenged as improperly obtained and a violation of the person's Fourth Amendment rights to unreasonable search and seizures.
The defendant can then get that evidence thrown out of court under the "fruits of the poison tree" doctrine that states if a search is illegal, then anything that is obtained is also tainted and is unable to be used as evidence. This is pursued by the defendant's attorney filing a "motion to suppress" to have the evidence thrown out.