As others have said, you're correct. Many native speakers have a habit of using "there's" when they mean "there are," probably because it's easier to say the one-syllable contraction "there's," and there is no contraction for "there are." Even highly educated people sometimes make this mistake in casual speech, though usually not if they're speaking in a more formal setting.
As far as I've noticed, this only happens with the contraction. For example, you'll never hear anyone say "How many people is there?" That's obviously wrong. But in casual settings, you'll hear many native speakers say "There's three people."