1) If the filter is at the back, since the air is pulled through it, the dirty side is outside where people and kids can touch it as it builds up. If the filter is in the front, the dirty side is inside (towards the fan blade) while the clean side is outside.
2) If the filter is at the back, due to air's resistance it is possible, due to nooks/gaps in the fan, that the some of the air may be pulled from elsewhere and not all the air may pass through the filter. If the filter is in the front, it is easier to seal between the fan and the filter to make sure all air is pushed through it.
I'm curious... doesn't #2 cut both ways? i.e. if you can seal the front, you can seal the back?
I wish the guy on the video would take an air reading measurement near the side of the filter. I'm guessing that a lot of unfiltered air is escaping out the sides.
BTW you need not cover the entire area of the fan with filter material. So, for instance, if your fan's breaker is shutting the motor down b/c of the load of the filter, you can slide the filter up to cover less of the fan with the filter, reducing the load on the fan motor. While not all air passing through the fan will be filtered, over time most air will eventually pass through the filter and the room will be cleared of particulates.
Similarly, it is not necessary that the filter be the same shape or size as the fan, since with each pass at least part of the airstream is cleaned. Eventually all the air in a room will pass through the filter area.
With the filter thoroughly taped to the front (nearly airtight), there’s a large amount of blowback. I suspect that this is reducing the overall efficiency of air filtration.
I used to put the high-efficiency filters on my furnace, my HVAC guy said these filters are so heavy that they put a strain on the blower motor. It's better for the motor to use a plain blue fiberglass filter (MSRP $1). You're not really filtering that much out of a closed house, unless you run your forced-air A/C or Heat with the windows open.
This graph of airflow vs. MERV rating isn't very conclusive in my mind: http://www.homeenergy.org/UserFiles/file/26-6_p34big(1).jpg
Granted there are about a million variables in all HVAC systems that could affect the results.