An Pluiméir Ceolmhar is correct. Glottal stops are often used in American English to separate words, where the first word ends with a vowel and the next word begins with a vowel. Try saying "Happy Easter" without a glottal stop and the words run together – "Happeeeester." The glottal stop is more likely to be used when you are trying to speak very distinctly or in a dignified manner. It sounds sloppy without, relatively speaking.

Most people are unaware of this. Elementary school teachers – from whom we get most of our ideas about "right" and "wrong" pronunciations – usually don't call attention to such things unless there is a "problem" – not everyone is pronouncing things the same way.

Glottal stops aren't difficult for Americans to pronounce; it's more difficult to get people to notice them.

By the way, I think Mark Cohen was pulling your leg.