Calling a rat a mouse, and buying the small traps. The traps never fire, the homeowner concludes the traps are bad, and the burrow in the yard keeps producing rats. If a rat trap is what the droppings call for, use rat traps, use plenty of them, and leave them baited but unset for a few days first.
Putting poison in the walls. Whether it is mice or rats, a rodent that eats bait indoors dies indoors. UC IPM and Penn State both say so, and the smell that follows is the call I get three weeks later. Bait belongs in locked stations outside, placed by a licensed applicator who follows the label, and nowhere else.
Sealing with foam, caulk, or steel wool alone. UC IPM says plastic screening, rubber, vinyl, insulating foam, and wood are unsuitable for plugging holes used by mice, and rats chew through plastic, foam, wood, and caulk. Metal and cement hold. Stainless steel scouring pads are a temporary plug at best.
Treating the yard as somebody else's problem. A rat job that stops at the foundation wall is a rat job that comes back, because the burrow is 20 feet away under the woodpile. Garbage in metal cans with secured lids, pet food brought in at night, bird feeders moved away from the house, and a 2 foot gap between shrubs and the foundation are the rat prevention list straight from UC IPM, and they are what keep the 60 days quiet.
Ignoring one mouse. UC IPM says a female can have 5 to 10 litters a year of about 5 or 6 young, born 19 to 21 days after conception, and the young are breeding in 6 to 10 weeks. The one mouse in October is a family by Thanksgiving. We covered the math in I saw one mouse, how many do I have.