Pawn and Two: <Knight13> Anderssen may have been tiring near the end of this tournament. This was the 22nd and last round of the Paris 1878 tournament. Anderssen scored 7 points in the first half, and 5.5 points in the second half. His 12.5 total was good enough for a 6th place finish.
This game was played on July 23rd, giving Anderssen little time to rest, as the Frankfurt tournament started on July 27th. Anderssen placed 3rd at Frankfurt, which turned out to be his last tournament.
In the book, "The Chess Games of Adolph Anderssen - Master of Attack", edited by Sid Pickard, he explains how difficult it was for Anderssen during these last tournaments in the summer of 1878. Pickard stated that Anderssen was <already suffering seriously from a disease of the pericardium>.
Anderssen's results were actually very good, considering the seriousness of his illness.
In the tournament book, "Der Internationale Schachkongress Paris 1878", E. Schallopp noted that 27.Qe4 was a weak move and recommended instead, 27.Nd2 with 28.Nde4 to follow.
My Fritz indicates the position would be about equal after: 27.Nd2 Rae8 28.Nde4, or 27.Ng3 Rae8 28.Bd2. Best for White, with just a small advantage was: 27.Bd2 Rae8 28.Rxe8 Rxe8 29.Ng3.
Take another look at your suggested 29.f4. After 29...Nxf4!, Black is clearly winning.
While Anderssen missed holding the position equal at move 27, Fritz suggests at move 29, White may still be able to survive with: (-.34) (22 ply) 29.Bd2! Rxe1 30.Rxe1 Nh4 31.Re3.
Regarding the final position, Anderssen took your advice and did not resign after 33...Bd2.
The tournament book states after 33...Bd2, <und Schwarz gewann>. Based on this statement, it seems likely some additional moves are missing.
In any case, Fritz confirms the position after 33...Bd2 is winning for Black: 34.Rc2 h6 35.Rxd2 Nf3+, or 34.Rc2 g6 35.Rxd2 Nf3+, or 34.Rc2 Be3+ 35.Kh2 Nf3+ 36.Kg3 Nxd4.