Definition of a False Prophet
False prophets are proven wrong:
Deuteronomy 18:21, 22 "And if thou say in thine heart, How shall we know the word which the LORD hath not spoken? When a prophet speaketh in the name of the LORD, if the thing follow not, nor come to pass, that is the thing which the LORD hath not spoken, but the prophet hath spoken it presumptuously: thou shalt not be afraid of him."
False prophets bear bad fruit:
Matthew 7:15-20 15 Beware of false prophets, which come to you in sheep's clothing, but inwardly they are ravening wolves.
16 Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles?
17 Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.
18 A good tree cannot bring forth evil fruit, neither [can] a corrupt tree bring forth good fruit.
19 Every tree that bringeth not forth good fruit is hewn down, and cast into the fire.
20 Wherefore by their fruits ye shall know them.
Is Harold Camping a False Prophet?
A false prophet is one who says "God has revealed new information to me and called me to reveal it to you." The false, or erroneous exegete merely says, "God has spoken in His Word, and I understand Him to be saying this..." In both instances we have a man saying God is saying something God has not said. In the latter, however, the Word of God in the Scripture remains the sole final and binding authority on men.
If being wrong about what the Bible teaches is the same as denying the truthfulness of the Bible, we are all guilty. Not a one of us is right about everything the Bible teaches.
Now the tricky part: While Camping claims over and over that his only authority is God and from Scripture alone, his means of understanding or interpreting the "spiritual things" of the bible really depend upon his own self as the sole final and binding authority. Perhaps more accurately, each person becomes their own authority not Camping specifically (though highly influenced by Mr. Camping and Family Radio programming). The end result is an attempt to make yourself God, without even being consciously aware. See Comparing Spiritual Things with Spiritual Things.
[Special thanks to RC Sproul Jr. for wording, thoughts and insight on this topic.]