"Can Black force a win from the resulting positions? "
Bobby Fischer thought so. The debate is still raging however, but the consensus is that white has no advantage in the King's Gambit as black has many ways to equalize quickly. Then again the Berlin in the Ruy leads to fast equality for black too but is far easier to play as white than the King's Gambit, and there's much less room of going wrong. In fact, the theoretical onus in the Berlin Wall is on black whereas it's on white in the King's Gambit.
Summary: Berlin Wall = easy equality for black, but black must prove he knows how to implement the thematic strategies and how to handle such positions. King's Gambit = easy equality for black at least, but white must prove he knows how to play such positions, such as making sure black can't make use of white's kingside weaknesses to improve his own position further and how to use threats against f7 to improve your own position (certain lines where this applies of course)
In chess, a mistake is a move that causes a drawn position to be lost, and a winning position to be lost or drawn.
Thus, is the King's Gambit, 2.f4 a mistake? Can Black force a win from the resulting positions? Assuming 1.e4 leads to a draw with perfect play, and assuming 2. f4 leads to a draw from perfect play, 2. f4 would not, actually, be a mistake.
I will set out to explore this possibility, using LiveBook and the world's top engines. We shall see what I uncover.