If you call someone a liar how can you then possibly trust that person with any sort of authority. This then means that either; Mr. Trump didn't mean what he said when he called Mr. Carson a liar, in which case Mr. Trump becomes the liar, or Mr. Trump is actually happy to have someone in his Cabinet team he can't trust. Either way after saying what Mr. Trump said about him he shouldn't have appointed Mr. Carson.
I believe Mr. Trump shouldn't have appointed Mr. Carson if he believed he was a liar. Even if Mr. Carson was good for the job, there was already heat between the two. Trump shows unreliability when he appointed a man he called a liar, showing that he is wishy-washy. These qualities do not look good as a future president.
It has nothing to do with their battles during the campaign. Opponents often appoint each other after the election, such as Obama appointing Clinton as Sec. of State. The problem with this particular appointment is that Ben Carson has zero experience to be running this post. He technically has zero experience to be running for president, but apparently that doesn't seem to matter...
No, Trump should not have appointed Carson to a Cabinet position after calling him a liar during the campaign. People say that what is said during a campaign should not be taken seriously, that it is just part of the campaign, but that's just not true. if you're an honest person, you should say what you mean and then follow through on it.