4 move checkmate

1 move e4      2 qh5    3 bc4     4 bf7

Ok, let's prove your analysis.

That does not look like a checkmate at all. It's a check in 4 turns, but not a checkmate in 4 turns.

The author only mentioned White's moves. He/she did not mention what Black's moves are, so if Black's move is something like what I have included, then there is no checkmate.

Even if you are going to actually try this simple and not very practical 4 move mate (it only works against rank beginners and very weak players), you would be well advised to play Bc4 on move two - rather than moving the queen out so early. 

1. e4 e5 2. Bc4 is called the bishop's opening, and it actually not a bad opening at all. Whereas moving the queen out on move two is very bad. Black simply play Nf6 and you are stuck beating a sorry retreat. 

No; 2...Nf6 in this case is bad.

2...Nf6 is bad because it allows attack on the f7 pawn.

Well yes, maybe putting a question mark to 2...Nf6 is an overstatement, but White's extra pawn should be slightly better than Black's good compensation of a "forced development" by 3...Be7.

Not in my said position above, 3. Qxf7+?? Kxf7.

Also, if 2. Bc4 is played instead, 2...Nf6 defends everything. Moves like Nf6 are very common in games.

Is the last move Bf7 or Bxf7 ?

Bf7.

Probably the opposite.

An opponent who has a reasonable chance of falling for the 4 move mate has a reasonable chance of reacting poorly to 2.Qh5

Also, after e4 e5 Bc4 Nf6 you've lost your chance to play Qh5.

So the Bishop moves to f7 and does not capture anything ?

Else we could have the knight on e7 and pawn on e5. Bxf7+ would work, but without a capture this is more difficult.

Chessiship you sure yideng agrees?

idk

I am 100% sure some players are lazy to include the notation 'x' for capture.

He spells out 2. Qh5 as 2. qh5, so I more or less see why he writes 4. bf7 instead of 4. Bxf7+. 

No; Qh5 can still be played (the chance is not lost yet since the White queen is still on board and the move to h5 is currently available).

You mean 3. Qh5 is not a plausible and logical move since it fails to 3...Nxh5.

Maybe he forgot the x and it is indeed Bxf7. I just left him a message. Else the answer is 1. e4 e5 2. Qh5 Ne7 3. Bc4 a6 4. Bxf7#

That's one of the only sequences ending in 4. Bxf7#. Most players who are able to play chess would probably go for 4. Qxf7# rather than 4. Bxf7.

Weaker players tend to play 4. Qxf7# because their mindset is, "Queen is the most powerful piece and I must use it to checkmate the opponent's king!".