Mouthwash often contains ethanol or xylitol — both toxic to dogs.
A typical bottle contains enough ethanol to severely intoxicate a small dog.
Many mouthwashes are 15–25% ethanol by volume. Some sugar-free versions also contain xylitol. Both can cause dangerous CNS depression, and xylitol additionally causes hypoglycemia and potential liver damage.
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Treat any meaningful ingestion as an emergency, especially in small dogs.