I think the Bc4 is a mistake. or rather a dubious move as it loses a pawn unnecessarily.
Is 7. 0-0 a mistake in the Najdorf Sozin Attack?

7.O-O isn't a mistake but it allows ...Nxe4 tactics at certain points in the game. I don't know much about those positions.
Black shouldn't try to win the pawn immediately because White gets good compensation. The same position can be reached after 7.Bb3 b5 8.O-O
http://www.chess.com/forum/view/chess-openings/sicilian-defence-fischer-sozin-dilemna

I'm pretty sure the whole ...b4 idea is not actually that bad. I remember Anand playing it as black back in the 90s. But the idea is not to grab the e4 pawn. Rather, black, after Na4, plays ...Bd7 and ...Nc6, trying to grab a solid position while playing against the awkward a4 knight.

I don't know what do you think.
The computer engine thinks the loss of the e4 pawn gives white an +1.09 advantage. Those silly computer that don't understanding opening's lol.
What are they looking at here. Do they not understand black just stole a center pawn?
I wonder what kind of compensation they are using to justify such a dubious castling moving.
I don't know! The fact white has 3 minor piece's developed, A castled king, and A Active rook attacking a undefended knight and indirectly facing an exposed uncastled black king.
No way that can't be it. Stupid computer engine's.
Black should be winning here he is up a pawn. Why does white have the advantage HA HA.
*I hope you catch that sarcasm in their becuase I'm laying it down pretty thick Alway's!*
I just want to share with you a game I played about 10 days ago.
7. O-O is not "the main move", Bb3 is more popular by far. My guess is 7. O-O is a bit dodgy but not unplayable.
X-Player I don't know how the text is appearing on your screen, but on a normal screen it looks way oversized. I find your computer analysis unhelpful and not funny.

7. O-O is not "the main move", Bb3 is more popular by far. My guess is 7. O-O is a bit dodgy but not unplayable.
X-Player I don't know how the text is appearing on your screen, but on a normal screen it looks way oversized. I find your computer analysis unhelpful and not funny.
I'm sorry but you are confused.
I didn't give you computer analysis. I gave you the computer evulation which was +1.09 advantage white.
The rest of what I said was my own analysis. An if it was not helpful than I'm sorry spaghettio.
Maybe you should read some books/watch videos which show what happens if your opponent just pushes pawns and moves the same piece multiple times in an opening.
Instead of getting developed and getting king safety.
To sum up: it is not a mistake. All you had to do is run this in chess explorer. Plenty of games where white castles and deliberately hangs that pawn, not even a single master game where black takes. The problem of taking is way to open h1-a8 diagonal or a significant loss of tempo in the opening where black does not even get a chance to castle.
No 7 O-O is no mistake, on the contrary 8...b4? is a mistake by black, as black is behind in development and his king is unsafe. White gets ample compensation for the pawn.

Play over this game before you reach any firm conclusions.
A Heroic Defense in the Sicilian Najdorf - Kids, don't try this at home! - Chess Forums - Chess.com

No 7 O-O is no mistake, on the contrary 8...b4? is a mistake by black, as black is behind in development and his king is unsafe. White gets ample compensation for the pawn.
I agree that White gets more than enough compensation if Black tries to snatch the e-Pawn.
As long as Black avoids the greedy 8. ... b4 Pawn-grab and plays 8. ... Be7 instead, I feel that the variation is nearly equal, but slightly better for Black.

Not sure if exact position but there was a Fischer v Tal game in "60 Memorable games" were white got plenty of compensation for similar pawn sac.

nah, in fact the main line 7. Bb3 usually transposes after 7... b5 8. O-O. The Sicilian is a very sharp opening where small lapses in development can have a big outcome on the game. The problem here is piece activity; black has one active piece, while white has at least three and a castled king. Even without looking at the board it's not hard to imagine that its sufficient compensation.
But! All of the refutations to blacks greet are difficult sacrifices. I would say that anyone below a high intermediate that has studied the lines for white thoroughly would fail to find the critical continuations. I would go digging around in the engine and opening book to check it out. White has like a 65% win rate after Re1 d5.
Or does White get any compensation for the lost pawn?