First of all, let's look at how they are dressed. Mac is wearing jeans, a white T-shirt, and a black vest sort of thing. His buddy, skullet and all, is wearing too-tight jeans and this hideous purple button-up shirt that is unbuttoned halfway down his chest. That's fine for like hanging around changing your black light bulbs, or maybe going out for a pizza, but those are not clothes that are conducive to moving. When one moves you get sweaty, dirty and your clothes have the potential to rip and tear on anything. The last thing I want is my disco shirt catching on a door handle as I haul my pots and pans into my new place. Plus, the sweatiness would muck up the silk.
Second of all is how they are going about it. He has a huge truck, way bigger than one would need for the average apartment, and they aren't working very hard to get it unloaded. They each brought one box up the stairs. I have moved enough in my life to know that if you are only taking one little box at a time you aren't going to make it. The box Disco Stu was carrying I would have had on top of the box MacGyver was carrying, and I would have had a floor lamp in my hand as well.
The again, this IS MacGyver, who am I to tell him how to go about his business? I mean, this is a guy who stopped a chemical explosion with a chocolate bar AND escape from East Germany like sixteen times all while helping kids in need. I wouldn't be surprised if he rigged up some way to like conveyor belt his stuff into his apartment with like a paper clip and some pantyhose. All I know is that his moving looked nothing like mine did. And his was a whole lot prettier.