To miscount is to get the number wrong: you count the people, the votes, the coins, and the total is not the true total. It can be an honest slip — you skip one, you count one twice — or, more rarely, a charged claim that the counting was done badly on purpose. There is also a noun, a miscount, meaning the wrong total itself. It is an ordinary, clear word; you will hear it with money, scores, and especially votes. It is not the same as miscalculate, which can mean the whole sum or the thinking was wrong, not only the counting one by one. Though actually, after a close election, people say miscount when they mean any mess in the tally, even if the real problem was a machine, a rule, or a pile of papers, not a person pointing at things and slipping.