That was a hell of a video. More good SF in that 3 minutes than any feature film I've ever seen. With the possible exception of Gorath.
There was actually a proposal for a Venus fly-by using a combination of Skylab and Apollo technology. Nobody would seriously propose such a thing today.
Manned fly-by missions are not practical. Costs too much when robot probes can execute fly-by missions much more cheaply and without risk to human life. No, you save your manned missions for when it's time to land and Do Shit. No machine yet invented or even on the horizon is as flexible and adaptable as a human on the spot. Speaking of fly-bys, tho, New Horizon is about to wake up from hibernation mode and is approaching Pluto for a fly-by in 2015.
Depending on the mission architecture you can do a Venus fly by on the way to Mars. Lengthens the trip to Mars by a few months but it is doable. Might be a nice way to piggyback and extra mission.
Yes, a strategy that's also been used in unmanned missions. The Galileo mission to Jupiter did something like that and so did Cassini out to Saturn. For that matter, New Horizon did one as well. The Voyager 2 mission included Uranus and Neptune fly-bys as "bonus missions." Not to mention the interstellar exploration that both Voyagers are now doing, made possible by the spacecraft remaining operational for far longer than anyone thought they would.