Yeah, his footwork, and technical ability to strike balls in a variety of ways seemed to save alot of strain on his body.
There alot of herky jerky movements at this level that look so unnatural for the body, but Roger always got himself in positions to make it look natural.
Constrast to the way Djokovic plays. He looks like gumby out there, and while Nadal has toned it down a little bit these days, I remember feeling pain just watching him lol.
The bolded part is key when it comes to Federer's success. I wouldn't call him quick around the court, but if you watch his side of the court (ignoring the opponent completely) you will notice two things that stand out the most.
First it's the anticipation and the ability to read his opponent. 9 times out of ten you will see that Roger places himself around the court in the way that allows him to take away the obvious angles. It's a probability play basically. He dares for you to beat him with a difficult shot.
The second, and the most important part (IMO), is his footwork. There has never been a male tennis player that set his feet even during the most difficult of shots as well as Federer does. Unless he's totally scrambling to put his racket on the ball, he never strikes the ball too early. Placing your feet properly to drive the ball is the most important aspect of tennis. It is that what drives precision and ball placement.
Lastly I want to mention his defensive backhand slice. It is very important to his game as it allows him to buy some time and re-group. Federer absolutely possesses a variety of shots, but it's this slice that is the most impactful to his overall game IMO.