Three comments.
First, it's not fair to say the director didn't know how a DA revolver works - it's pretty simple and Don Siegel wasn't stupid. He was however a director, and directors make movies for entertainment purposes, not gun training films.
It's a simple discontinuity error in the movie and the odds are the directors and editors were well aware of it, but just didn't care as they had other priorities.
It's a composite of two camera positions and you need to do it in separate takes so that a) you're not getting another camera in the frame and b) so you've got room to get the shot of Dirty Harry from the front. (Think about where the cameras have to be positioned for each point of view in the scene).
It's probable that they shot several takes from each camera position and then assembled the final scene with the best take from each point of view. It's also likely that Don Siegel noticed the discontinuity of Clint Eastwood doing a DA trigger pull after already cocking the hammer, but he obviously wanted the drama and effect of cocking the hammer, and/or the preferred Albert Popwell's performance in the hammer cocking take, while preferring Eastwood's performance in the DA trigger pull take.
The reality is that most people are not going to notice, and I watched the film at least half dozen times before I noticed that particular discontinuity, and then I was more interested in the revolver than the movie.
There are after all much bigger discontinuities in that scene. For example Harry walks through the spray of the broken fire hydrant and as he approaches the curb, the shoulder of his tweed jacket clearly has water droplets on it, yet at the end of the scene the jacket is dry. And of course despite also being supposedly sprayed with water, his Model 29 is also bone dry with no water drops visible on either side in the close up scenes. It either got wiped down and dried off between scenes, or he had a rubber gun when he walked through the spray. Rubber replica revolvers were used in the scenes in the Dirty Harry movies when a revolver was dropped, etc, as the Model 29s were needed in good condition for the close ups, so no Model 29s were harmed in the making of these movies.
Per the NRA, the producers and script writer planned on using a Model 29 with a 4" barrel but the Model 29 was obscure and while still cataloged by S&W at the time, was actually out of production as demand for it was almost non existent. The producers ended up using two revolvers, one with a 6 1/2" barrel and another with an 8 3/8" barrel that were assembled by S&W specifically for the movie. Demand went through the roof after the movie.
The 6 1/2" Model 29 used in "Dirty Harry" and "Magnum Force" was given to script writer John Milius - the man responsible for the .44 Magnum being used - by Clint Eastwood, and Milius has it on loan to the NRA Museum where it can be seen in the Hollywood Guns collection. They also have the Walther P-38 used in Dirty Harry.
For S&W fans the NRA Museum also has the Model 66 used in "Tightrope", the 639 and 659 used in "Reservoir Dogs", the Model 30 used in "Pulp Fiction", and Clark Gable's personal Registered Magnum on display.
Second, the "5 in 1" blanks originally used in the old westerns could be fired in a .38-40, a .44-40 or .45 Colt revolver or in a .38-40 or .44-40 rifles and carbines, thus the name "5 in 1". ( .45 Colt rifles and carbines were not available then, as the .45 Colt was not an original caliber in the Winchester rifles and Carbines.)
Sometime after WWII these brass blanks changed to preclude firing in a .38-40 chamber so they became "3 in 1" blanks but the "5 in 1" name still stuck. Once the .45 Colt started being produced in replica Winchester rifles and carbines, it became a "4 in 1" blank, but still retained the "5 in 1" name.
Modern "5 in 1" blanks are slightly re-profiled to allow use jin the .44 Special and .44 Magnum making them a "6 in 1" blank (7 in 1 if you count the .410 shotgun).
However, when Dirty Harry was filmed in 1971, these newer 5 in 1 blanks were not available. Fortunately, it's never been hard to make a blank for a pistol cartridge, and doing so poses no great expense or time factor for a major movie production (compared to a weekly television series) and as this was the approach taken, with "Dirty Harry". There was never a need to use a Model 25 revolver to stand in for a Model 29 to accommodate the 5 in 1 blank because 5 in 1 blanks were not used in the movie.
I think the association with movies and the 5 in 1 blank, that did not at the time accommodate the .44 Special or .44 Magnum, is what has led to this idea that a Model 25 was used. That at least makes more sense than the rumors that it was a Model 57 in .41 Magnum.
If you watch the "do you feel lucky" scene near the end of the movie with Andy Robinson you can see the ".44 Magnum" marking on the barrel clearly showing that the revolver is indeed a Model 29.
Finally, if you want to start arguments about Dirty Harry movies, bring up the scene in "Magnum Force" in the indoor target range where Harry states "I use a light special. With a gun this size and weight it has no more recoil than .38 out of a .357."
Some folks will say that was just his load for fast shooting in the upcoming match while others claim it meant he carried .44 Special, not .44 Magnum.