Obviously there are multiple scientific problems with religious prophecies, but this in my opinion is the biggest flaw because of my love of math and understanding of probability.
1. Most religious prophecies do not give exact year.
Not giving an exact year means that the prophecy has an unlimited amount of time to "come true". Given enough time anything can be accomplished. People predicted almost 1000 years ago that humans would have the scientific technology to fly. Eventually humans were bound to have that technology given enough time. Just like now people predict that humans will have access to faster than light space travel. Eventually science will get there given enough time. These however are not prophecies of any kind.
2. The "Infinite Monkey Theorem"
The Infinite monkey theorem states that "[a] monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare." This same thing applies to religious prophecies. Because of how probability works if you have an infinity in the ratio the probability is always guaranteed no matter how unlikely it may seem.
Naturally ever scenario or combination of scenarios given in a religious prophecy will eventually occur within an infinite amount of time. I could be "enlightened" by Santa Claus that eventually a Wookiee wearing a top hat will be born of a clown-type creature and attempt rule the world. Unlikely to happen in my life time, but eventually given an infinite amount of time this WILL happen. But I'm not a prophet nor am I enlightened by God or some supreme being.
3. The Vagueness of religious Prophecies
Every prophecy that religious people claim has come true is a prophecy that is so vague that it is more likely to happen sooner than my Wookiee prophecy. The Mayan prophecy, Pagan prophecies, even comic book prophecies by Batman. In order for any scientific person to take a prophecy seriously and accept it as real the prophecy would have to be very specific with a time(day, month and year), the place, the person (full name of the person), detailed description of person or event and cannot be something that is predictable by scientific evidence.
Scientists make accurate predictions all the time, because it's science. But scientists don't normally claim to be magical prophets.
4. Self fulfilling prophecies and past prophecies
Many religions attempt to set out and force a prophecy from their religion to come true. It seems that religious fanatics are always trying to make their "End of the World" prophecy come true by starting a war that could actually end the world. Setting out to ensure something comes true does not make it a prophecy.
More laughably there are religious prophecies given about a past event that already happened or give a prophecy in the same book they claim it came true. Like if I write a book about my Wookie Prophecy and then claim it came true because I wrote in the same book that "A long time ago in a galaxy far far away" this sort of thing happened. With no way of disproving my prophecy we have a Russel's Teapot fallacy.
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