The line with 1.d4 d5 2.e4 dxe4 3.Nc3 Nf6 4.f3 exf3 5.Nxf3 e6 is generally known as the Euwe Defence.
Black blocks in the c8-bishop but increases the control over the d5-square and prepares to counterattack against d4 with ...c7-c5 or ...Nb8-c6. White normally pins the f6-knight with 6.Bg5 and Black normally parries the pin with 6...Be7, for while the immediate 6...c5 is playable, it does not present White with any trouble getting enough compensation for the pawn.
Traditionally the most popular move is then 7.Bd3, aggressively eyeing the h7-pawn and thus making the immediate 7...0-0 inadvisable (while it doesn't lose by force, White gets an extremely dangerous attack with the standard moves 0-0, Qe1, Qh4 etc, and 8.Qd2 and 8.Qe2 intending 0-0-0 are also playable). More challenging is 7...c5 but then after 8.dxc5 Qa5 (or 8...Nc6) White can consider 9.Qe2 and 9.Qd2, as well as the main line 9.0-0.
My problem with 7.Bd3 is that Black can take advantage of White neglecting the defence of the d4-pawn, and also threaten to chop off the bishop by playing ...Nb4, by playing 7...Nc6.
What does White do about the attack on the d4-pawn and the threat to take on b4? Of course Black cannot take on d4 immediately because of Nxd4 and if ...Qxd4??, then Bb5+ picks up the queen, but the threat lingers over White. Christoph Scheerer made a case for 8.a3, preventing ...Nb4, but I think it may be too slow to give White full compensation for the pawn, and 8.Qd2 Nb4 allows the trade of the d3-bishop. This leaves Lev Zilbermints's preference 8.0-0, sacrificing the pawn (since 8...Nxd4 9.Nxd4 Qxd4 is check) and intending 8...Nxd4 9.Kh1. This line is likely to be effective at fast time limits but I think that objectively Black can get quite a large advantage after both 9...Nc6 (recommended by Craig Evans at the Chesspublishing.com forum) and 9...c5 (which I discussed at length with Mark Morss and a few others under the name "SWJediknight")- the discussion can be found at http://www.chesspub.com/cgi-bin/yabb2/YaBB.pl?num=1133589453/195
Therefore I recommend that White instead plays 7.Qd2 and I cannot find a way for Black to stop White from generating enough of an attack to compensate for the pawn. If 7...h6 then 8.Bf4 works out quite well for White, and if 7...0-0 then White can probably get enough play with both 8.0-0-0 and 8.Bd3. Castling queenside means that in many lines, ...c7-c5 and ...c5xd4 can be met by Rd1xd4. My in-depth analysis of 5...e6 is featured in the third illustrative game at http://tws27.50webs.com/chess/blackmar_diemer_gambit/bdg4.htm
Therefore I don't regard 5...e6 as particularly worrying for BDG fans from a theoretical perspective. The other three main lines, 5...Bf5, 5...g6 and 5...c6, however, may be a different matter.
In the meantime I have ordered John Shaw's "telephone directory" of a book on the King's Gambit- it will be interesting to compare his conclusions on the opening with mine, especially as we appear to have common ground (his main recommendation against the early ...g5 approaches is the Quaade Gambit, which I currently consider to be the most promising option for White). I hear that he regards 1.e4 e5 2.f4 exf4 3.Bc4 to be refuted by 3...Nc6, but as Stefan Bucker noted at Chesspublishing.com, this depends on whether or not Black can get an advantage in the Hanstein Gambit lines that follow 4.Nf3 g5, as well as the 4.d4 lines. I'll reserve judgement on this until I get my copy of the book, but I was unable to find a route to advantage for Black in my online analysis of the Hanstein, and from a practical perspective, I can say that I've had several more online games as Black in the Hanstein recently and the resulting middlegames have usually been dynamically equal.