A day has 24 times 60 equals 1440 minutes, which means that you have to watch 200,000 videos each of 1 minute, it will take you 138.8888… days (about 4.67 months) to do this. At least if you are watching non stop. But since a human has to sleep around 8 hours a day, one should be able to watch for up to 16 hours a day. Under this assumption you will need 208.333… days (about 7 months) to complete the task.
Of course, even 16 hours a day non stop watching videos, is a very unrealistic scenario. A more realistic scenario would be watching videos for about 10 hours a day, 5 days a week, which would allow you to watch 50×60=3000 videos a week. An in order to see all 200,000 videos would take you 66.67 weeks.
Question: who would actually do such task in the first place? The answer: the people behind Mars One. On September 9th, 2013, they claimed to have received 200,000 applications for a one-way trip to Mars. As part of the application procedure, people had to submit a one-minute video. According to September press release, these 200,000 applicants were to be screened by the Mars One Selection Committee, and that the procedure would be finished by the end of 2013.
But as we have seen, it’s very unlikely that the committee could have watched all 200,000 videos within a year. Of course, the committee does not exist of one person, but even if they had three members, who would each watch a third of the videos, it would take them 22 weeks to complete their job. But given the importance of the selection, would you base your decision to select (or not) one for a Mars mission on the judgement of a single individual? No serious space agency would base any decision of importance on a single judgement, at least two persons should be involved.
Yesterday Mars One has announced to have selected 1058 candidates for the next selection round. According to the Dutch Public Broadcast, Mars One has not revealed any details about the selection procedure. So we cannot verify whether they have watched all application videos, but we expect they have not done so, given the very unlikelihood of this. Personally I believe the people of Mars One have simply taken a random sample of all applications, and have based their selection upon the sample.
The fact that they keep their selection procedure secret, might be an indication that something is stinking at Mars One. I rest my case.