Learn to just walk away and fold at times if you know what's good for you, and don't underestimate your opponent, ever. Remember you cannot win all the time, especially if you're just starting.
This isn't so much of making a mistake in poker but `getting what you wish for.` When a player wins a tournament trip out of the country and busts out on his/her first day, was the trip worth it?
In canada, I won a tournament trip to Australia but I was not able to get my passport updated in time so I couldn't go. Assuming I can win a trip to such a tournament again, are the trips easy or are they hassle ridden? I've had other free trips where I would have paid not to go.
For me, the worst mistake would be playing outside your bankroll. This is the surest way to stay broke. Research BRM and stick to the guidelines. Second, playing too many hands out of position. Third, over valuing big hands and not having enough discipline to fold them in unfavorable situations. Fourth, not paying attention to the table and the rendencies of your opponents and only playing according to your hole cards.