Other mistake: After killing his inmate, notice the blood on the inmate's neck is present in great amount. After camera changes, the blood is only on the shirt, the neck is clean with no holes nor coagulated blood. (00:51:00 - 00:51:45)
Other mistake: When Clyde is in the van driving back to the prison he encounters a road block. He evades this by driving down into the parking garage. There's no way that the police or SWAT would have missed this loophole. (01:32:34)
Answer: To make sure he was placed in solitary confinement. The warehouse that he owned and operated out of that was next to the prison also had a tunnel connected to every cell in the solitary wing. Clyde needed to be in one of the solitary cells so he could leave the prison whenever he needed to unnoticed, which also served to make it look like he had an accomplice on the outside.
Phaneron ★
When Nick is talking to a spook later in the movie, he is quoted as telling Nick: "That cell-mate that he killed, you think that was random? No. That's a pawn being moved off the board. Anyone who had anything to do with that case, he's gonna be coming after you." Just as all deaths played roles in Clydes game, as the audience we are led to believe this inmate played a role, but were never given any resolution as to what significance it was. Not a big deal in grand scheme of things, but unexplained.
I don't know if you just didn't read the answer thoroughly or if you didn't pay close attention to the movie, but Clyde killing his cellmate was far from being unexplained. He can't leave the prison if he's in a regular cell with the general population, so he kills the cellmate in order to get placed in the solitary wing, because every solitary cell is connected to the tunnel in his warehouse that is next to the prison, which allows him to leave whenever he needs to.
Phaneron ★