Most people seem to think it would be very rapid, and cite examples -- people caught on camera, operators of vehicles.
I'm not so sure:
People who are talking to each other on the phone would go, "that's odd" but I think would shrug it off as "boss came around" or "doorbell rang." Most wouldn't realize that something had happened until they failed to reconnect. But it would be odd, most quick disconnects are accompanied with a "Gotta go"
People on facetime/skype would be confused: The view suddenly shifts and the device is dropped. I think many of them would just think "Butterfingers..." but when the camera showed only ceiling, no noise, they would be aware that something happened. I think most people would make a semi-rational scenario for at least a few hours.
People who were physically present in the same room -- meeting, classroom, etc, where you know a lot of the others would notice right away. But picture the conversation when you call building security and say that someone evaporated giving a power point presentation. Strange looks. Water tests for mind altering substances. Lots of statement taking. And who does security report to? I think that each level it goes up the chain will require several hours of "Yeah right" "You don't say"
It won't get real consideration until one person gets reports from several places. Up to that point it's a "Mary Celeste" story. Odd. Unexplained. But unless you are family it's going to be a 15 minute sensation.
Some alterations of your scenario could keep it quiet for longer:
- Skip anyone moving faster than a walk. This eliminates most of the moving accidents.
- Skip anyone within 3 feet of a computer monitor. This eliminates anyone on a phone. or in front of a computer screen.
- People vanish in clumps. A room full of people at a time.
- People in the open, in sight of other people are left alone.
- People are taken with what they are holding. There are no piles of clothes, no phones lying on the ground. No, your car doesn't go with you. (Or maybe it does? Hmm.)
The clump vanishing means that the entire dev team meeting for a code walk through is gone, the entire congregation of the West Horsebiscuit Dutch Reformed Church is gone -- or at least everyone in church that day; Mrs Smith's Grade 12 lit class; Parents vanish in pairs unless sleeping in separate rooms. Bus loads of people, but only when the bus is at a stop or light in a fairly deserted area. Restaurant full of people one instant, gone the next. Waiters in the kitchen left, ones in the dining room gone. Whole families and groups except for the ones in the washroom.
This makes for a bunch of odd events.
The dev team isn't noticed until someone later is missed at another meeting. Bunch of living partners will probably wait a day, "He went out for beer with the boys" but not get really concerned until the next morning.
A missing church congregation is really unlikely to be noticed. Usually whole families will be gone. There will be a bunch of kids marked absent, a bunch of adults who aren't at work. Probably a few people who weren't in church, who complain about people that didn't come home.
Kids who wake up to find their parents gone will range in reaction. Some teens will think, "Great, the house is mine, at least until they come home" Some kids will get themselves off to school. Young kids won't know how to report missing people. Parents who wake up to find "the twins" gone, but Susan still in the house will have reactions depending on the age of the twins ranging from, "What are those two up to now?" to "Sneaking off to their trapline again..."
Class in school will be noticed the next period, at class change, but the next class in that room won't report it; however the noise will likely get someone from administration in, who finds no Mrs. Smith. It will take a while to realize that Mrs. Smith isn't on the school grounds any more. A raft of absent slips over the next few classes will convince the admin that something is wrong. But if it was the last class of the day, it will be supper time before parents start contacting the police, "Mike didn't come home after debate practice last night"
In this sort of scenario I think it would take several days to connect the dots at a town level, and a week or more at the national level. A town of 10,000 will have about 7 missing people. Which may mean some towns are missing a classroom, other towns are business as usual. A city of 100,000 loses 70 people. A bus found empty at a bus stop in suburbia, a missing group from a meeting, an empty MacDonalds.
You're the watch officer for Precinct 6 in East Horsebiscuit. You've gotten an odd call about a disappearance. Dispatch sends an officer to check. It's only as reports trickle up through the system that you realize something is really wonky. A precinct in NYC typically has 100-130 thousand people (77 precincts, 10 million people) So they are missing 70 to 100 people, but many of these will trickle in. By the end of the shift something is clearly going on, but it will take another day to realize there is a real problem, then another two days to get a good handle on the scope of the problem. I bet, however that each city will think that it's a local problem.