Is improved sanitation a good way to reduce most bacterial infections?

Yes: Keeping clean, cooking food thoroughly, and staying away from sick people are reliable ways to reduce bacterial infections. A bath or shower washes away bacteria than cause impetigo. Washing hands after using the bathroom (and washing hands before eating) helps prevent infections like typhoid and cholera. Not getting cough or sneezed on helps prevent illnesses like strep throat and whooping cough.

Certainly yes: Viral infections and parasitic infestations as well.