Predictions fall victim to "false accuracy", which is what the comments here are working to rule out. Predictions are only as valid as their specifics. A general prediciton can fit so many differnet events that it's effectively meaningless; any prediction must be specific to avoid this. For example, consider the following statements:
1. Something bad will happen somewhere at some time.
2. Something bad will happen somewhere within the next month.
3. A plane crash will happen somewhere within the next month.
4. A plane crash will happen in Germany within the next month.
5. A 767 will crash in Germany within the next month.
6. A 767, tail number NB-467, will crash in Hamburg, Germany, at 4:15PM (local time) on the 30th of April.
Now, 1 to 3 are so general as to be useless. They don't prove anything. The situations they describe are true more often than not, just by chance. Starting at 4 it gets interesting, but only somewhat. Predictions like number 4 could lead to statisitical proof, if enough of them were made and they held true. The same with 5, although it's quite a bit more specific and thus would be easier to prove statistically. Number 6, once you're cleared of any possibility of terrorist actions or sabotage, would go a long way towards convincing me of the possibility of precognition.
But that's the problem. Most predicitons fall into the ranges of numbers 1 to 3, especially dreams. A person dreams of someone close being hurt, for example. At almost any point in my life, someone in my family (brother, parent, uncle, cousin, close frined of the family, etc) has been ill or injured. Unless you can place a time limit on the dream, or specifics that are predicted, rather than an after-the-fact "Hey, I dreamed that!", it's uncertain.
There's also the pragmatic way to look at it. It's precognition if you have enough information to prevent or modify the outcome of the prediction. If your dream is so vague that no realistic measure could be taken to affect what you dreamt of, it's not precognition.
Especially with dreams, as well, you have mental factors. The easiest way to avoid those is to write down dreams as soon as you wake in the morning, keeping a journal, and write down as much detail as you can. Dreams, by their nature, are vague and fluid (most often). The mind fills in the details to join disjointed images and thoughts into a story of sorts. It's VERY easy, after the fact, for the mind to continue to embellish the memory of the dream by plugging in details. For example, a vague dream of danger to a loved one can easily become, in the mind, a dream of predicting a car wreck for your wife after the event (the wreck) has actually happened, even though the dream may have been nothing but the vague feelings with no details.
