The problem of the Rambam.
The problem is that it looks like that if you take the Rambam together with the Gemara you get a different halachic decision than if you take him on his own.

This seems to be the problem that Reb Chaim Soloveitchik is coming to answer.
An example is the Rambam in laws of forbidden sexual relations. In the case a person jumps into a mikvah before his is dipped for the sake of avdut (slavery) then he becomes free- but only if he was bought from an Akum (gentile). The problem is that the Rambam says if he is bought from an Akum the Israel still has kinyan Haguf (possession of the body). To put in arbitrarily the distinction of a mikvah like the Kesef Mishna does does not seems very much like it according to the simple peshat in the Rambam. But Reb Chaim makes a distinction here that makes sense. If the Israel buys the Akum from himself he has Kinyan Haguf completely because the akum can sell himself. But buying from another Akim he buys the kinyan Haguf that gives him the right to dip the akum into the mikvah for the sake  of advut.

So the Rambam comes out exactly like he says. The simple peshat (explanation) in the Rambam is the true peshat (explanation) and yet it is accord with the Gemara also!

This is according to my basic impression that the Rambam wanted to be able to be read on his own without looking at the Gemara.

In spite of the fact that the Rambam wanted to be learned on his own still people that read the Rambam without the proper Gemara background have just enough knowledge of Halacha to mix everything up without knowing they are doing so. And it is easy reading. A million times easier than the Talmud. So people can pretend to understand and fake their way.
Perhaps the Rambam was addressing an audience of people that already had basic Gemara concepts. and could read Gemara simply and plainly as opposed to the general Baal teshuva today.