Didn’t the guys on Bonanza wear the same outfits on every show? I can imagine them filming years worth of exterior shots in one day- riding up to the saloon or the sheriff’s office in various combinations of characters and in various degrees of urgency.
Also, some shoots use the same location dressed in various ways - for example, you might use the same office and shoot from a different angle and change out the furniture to be a different office. So of course you’ll shoot it all one way first and then the other way.
It’s “Rope.” Not “The Rope.”
The original statement was “The difficulties encountered … would be more or less the same today if you shot it on film” (emphasis mine). That acknowledges your point about digital rather than overlooking it.
Castaway had Tom Hanks start overweight (above his normal weight, IIRC ~30 lbs heavy) then lose that weight down to an emaciated state while growing his hair and beard out, and getting tanned, then shaving the beard and cutting the hair for his return to civilization. Tom Hanks actually went through that process, and it was his real hair and beard* in the film. That film would have been a lot less convincing if it was filmed out of order.
Although scenes within the timeline at various points might have been out of order with each other.
*I saw pictures where he hosted some awards ceremony thing during that time wearing a tux with that hair and beard.
I heard in an interview (with Charles Martin Smith, I think) that Spielberg shot American Grafitti in sequence because he wanted the actors to reflect the emotional and physical exhaustion of a single eventful night.
ETA: After checking IMDB for American Graffiti: “The film was shot in sequence, so as filming went on and the actors grew tired from the shooting schedule, the characters they played would also look more and more tired as the night went on.”
Too late to edit: And of course, I should have said Lucas instead of Spielberg.
What’s more, they filmed the early scenes (with him a little pudgy) and then took a break for IIRC an entire six months, while director Robert Zemeckis went off to film What Lies Beneath. This gave Hanks time to lose weight and grow out his beard.
Another vote for everyone to see Russian Ark. It really is a remarkable achievement.
Came in here to give this example also. Though, strictly speaking, it took I think 3 takes according to some of the special features - but the last one was beginning to end with no breaks. And I definitely agree it ought to be seen. One of the last scenes has the camera moving through a ballroom full of dancers - that they could get that in one take is truly astonishing.
Besides the locations already mentioned, they can schedule actors who do not appear in every scene can be scheduled for only a subset of the shooting days,. which means they don’t have to get paid for sitting around every day of production.
There are also more location switches than might be apparent. In one case the shots inside the school gym and those in the hallway outside the gym were done in two entirely different locations (and different days.)
Heck, even within a single set/shooting location its more efficient to plot out where the camera will be on every shot and rearrange the shooting order to minimize equipment moves.
This does assume that the shots are storyboarded or planned ahead somehow. Some directors/DPs make up shots on the fly.
Just wanted to add what Michael Caine mentioned in his autobiography: he worked with a director who jumped ahead in the script to shoot the actors-riding-around-on-horseback stuff first – because, hey, if you fall off and break some bones and can’t film the rest of the movie, they’ll have to junk whatever they’ve already shot and start over with a new guy, right? So, to keep costs down, they’d prefer to shrug and make that substitution on, like, Day Two…
Slightly off-topic question about live television.
Are some scenes filmed ahead of time and then shown to the studio audience? Scenes that come to mind from Seinfeld include street scenes, the swimming pool scenes, and the tennis court scenes. Places where building a set would be unwieldy.
This becomes most obvious watching a car chase scene in a city you are familiar with - you often see the cars racing past landmarks that are nowhere near each other.
Film making (moreso than TV) is about collecting shots that are the building blocks, and then assembling them in editing. Sometimes it is very mechanical, a frequent technique is to spend some time getting closeup reaction shots from the individual actors - basically just making faces to express a variety of emotions. These can then be cut into the scene in editing where appropriate.
Yes. Sometimes they are shown to the studio audience and the audience reaction is recorded to go with the scene.
Ann Morgan Guilbert, who played Millie on the Dick Van Dyke Show, said something just like this. She was paid only for the scenes she was in. She said, in the third year they offered her a contract and she refused. Carl Reiner was puzzled as why she wouldn’t want it. She said, if she had a contract, they would make her come in and sit and do nothing or give her a tiny part. She said, she was busy with her family and other TV projects and just being paid for only when she was needed gave her freedom.
In Australia’s great soap opera Prisoner (Prisoner: Cell Block H) Val Lehman, who played Bea Smith explained they always shot all the scenes in one location at once. This was done because the scenes were reused. The recreation room would be remade up as the governor’s office or the library.
She said, it was awful sometimes as you may come in for two straight days and do nothing but scenes in the dining room, meaning you were eating breakfast, lunch or dinner for two days straight.
Also kids are only able to work so much. Kathy “Sissy” Garver of Family Affair scenes with Buffy and Jodie would be shot first and quickly. Then she would be cut in later on as she was over 18 and could be on the set long hours. She said, often her heartwarming talks with Buffy were to a prop guy smoking a cigar. 
For the same reason nude scenes and sex scenes are usually the first scenes shot. This is so if one of the actors/actresses involved decides to back out they can be easily replaced without alot of footage having to be reshot. One notable exception was The Reader where David Kross’s nude scenes are among the last to be shot because he was only 17 when filming began.
Both Bewitched and I Dream of Jeannie where filmed this way because of all the special effects involved which made use of a live studio audience impractical.
So if you wanted to shoot in sequence, but did not want to move from set to set and back again, but did want to have a variety of sets, you’d put a steady-cam on your shoulder, and walk for an hour and a half through the Hermitage and three-hundred years of living history enacted by a couple of thousand costumed actors and a full symphony.
If you ever get a chance to view Russian Ark . . . it is a remarkable achievement.
If you are talking about digital cinematography, one of the SD card would be filled up in a few minutes if they could even handle the data rate. The Codex Digital holds 10 Terabytes of storage.
http://en.wikipedia.org/wiki/Codex_Digital
(pause to let my mind boggle)
I wouldn’t be surprised if even a lot of TV Productions use very high data rates so they can do editing on the uncompressed footage.
In addition to what others have mentioned, shooting in sequence can give the actors more time to become comfortable with each other. This may or may not be important, depending on the actors and the roles.
In the director’s commentary to Bend It Like Beckham, Gurinder Chadha mentions that they shot all the nighttime scenes first. (I think because the movie was made on a tight budget and doing night scenes involved a more elaborate lighting set up.) Anyway, there’s a nighttime scene late in the movie where Chadha said she was pleased by how good a job the actors had done of seeming like they knew each other well and had complicated feelings for each other when IRL they had in fact barely met at that point.