(not DVD order, and not TV airing order - but filming order)
The Firefly DVD commentary indicates that:
1 was Serenity (the DVD pilot)
2 was The Train Job (the TV pilot)
14 (last) was The Message
I assume the other episodes (that aired) were filmed in the order that they aired - but I could be wrong. Even if I'm right, where in that order were the unaired episodes filmed?
Extra credit if you can provide actual filming dates.
TV shows don't really film episode by episode, other than for such as a pilot, which will probably have been made months ahead of the main series.
They film in blocks, where one Director, 1st AD etc will be given control over 2, 3 or 4 episodes and they will film them interspersed, depending on actor availability and location requirements.
So... they go to the required location, taking the required principals, the whole crew and all their gear, and over a day or a week, they will shoot everything needed for that location for the entire block. This applies equally to whether the location is out in the countryside, or simply 'Studio 4' rather than 'Studio 1'.
A show with a lot of episodes per year and a short lead time will operate a 'rolling' style of production, where at any given time some episodes are being written, shot, edited like a production line. Eastenders famously broadcasts 4 shows, 2 hours a week [more over Xmas/New Year] and is shot continuously over 50 weeks of every year. Even with that type of schedule, it is still actually handled in blocks, with one director/1st/script supervisor etc for each block.
Anecdotally, they usually only shoot Monday to Friday for the regular schedule, with occasional Saturdays as 'pick-ups' for scenes they didn't get time to shoot, or they need to change in some way.
On those days, consecutive scenes can involve a complete change of Director/1st/scripts; though the other crew will be on set for the entire day. Depending on availability, often the cast will have to wait around for their next scene, because the director's time on a show such as that is more important than that of the principal characters ;)
For any show, completion dates will be subject to a similar set of rules as shoot dates. Once a block has completed principal photography, the director, editor, CGI team then do the same job again, on all that block. [I'm oversimplifying] but to think that shows are done in any kind of linear fashion is to misunderstand one of the fundamentals of the industry.
tbh, I don't know the specifics of Firefly - I work in the UK not the US anyway, but shoot schedules are the same the world over - dependant on budget, lead time, cast availability, location availability etc
Take something like Mr Selfridge, with big, complex sets... All the floors of the Selfridge store were the exact same set, but re-dressed each time to look like different floors. So.. they had to shoot every scene on each floor before they re-dressed the set to be a different floor of the store. That meant they were shooting parts of every episode for the entire season in one month... then they'd go off to do some location work for a couple of weeks whilst the set was re-dressed for another floor. Rinse and repeat until they'd got every scene for every floor. That's economics in action.
There were 26 episodes in the second season of Star Trek: Enterprise, an American series which aired about the same time that Firefly aired. Memory Alpha gives production dates for four of them.
"Dead Stop", directed by Roxann Dawson, was filmed 12 to 20 August 2002 & aired 9 October 2002.It is listed as the 30th episode produced. https://memory-alpha.fandom.com/wiki/Dead_Stop_(episode)
"Vanishing Point", directed by David Straiton, was filmed on 2 October to 10 October 2002 and aired on 27 November 2002. It is listed as the 35th episode produced. https://memory-alpha.fandom.com/wiki/Vanishing_Point_(episode)
"Precious cargo", directed by David Livingston, was filmed between 11 October & 22 October 2002 & first aired on 11 December 2002. It is listed as the 36th episode produced. https://memory-alpha.fandom.com/wiki/Precious_Cargo_(episode)
"Regeneration", directed by David Livingston, was filmed 27 February 2003 to 8 March 2003 & it first aired May 2003. It is listed a the 48th episode produced. https://memory-alpha.fandom.com/wiki/Regeneration_(episode).
The production dates for "Vanishing Point" and "Precious Cargo" Indicate that they were filmed as consecutive individual episodes instead of as part of a block of several episodes.
The production codes for the 2nd season Enterprise episodes seem to indicate their production order and thus that they were produced one after another. https://en.wikipedia.org/wiki/List_of_Star_Trek:_Enterprise_episodes
Thus it seems probably that episodes of the second season of Star Trek: Enterprise were produced about the same time as the Firefly episodes, and were produced one after another with a specific order that is knowable.
A list of episodes of Firefly here: https://en.wikipedia.org/wiki/Firefly_(TV_series)#Episodes also gives production codes, which sometimes indicate a different order than the broadcast order. Thus the production codes seem to indicate the production order of the Firefly episodes.
But a Firefly specific site would be the best place to ask about the production order of Firefly episodes.
