Human toothpaste often contains xylitol or fluoride — both toxic to dogs in adequate amounts.
Always use a dog-specific toothpaste; never share human toothpaste.
Many sugar-free human toothpastes contain xylitol, which causes dangerous hypoglycemia and liver injury in dogs. Fluoridated toothpastes contain about 1–1.5 mg fluoride per gram; large ingestions can cause severe GI signs and cardiac arrhythmias.
Sources
Any ingestion of xylitol-containing toothpaste is an emergency. Small fluoride exposures usually cause only mild GI signs; large amounts (a whole tube) warrant veterinary care.