As with the vast majority of so-called "contradictions" in the Bible, this one adds up to nothing up to nothing more than a failure on the part of the critic to read the text closely. Let's begin by looking at Numbers 25:9,
"And those that died in the plague were twenty and four thousand."
Now, let us note that I Corinthians 10:8 says,
"Neither let us commit fornication, as some of them committed, and fell in one day three and twenty thousand."
Compared side by side, what should be obvious is that Numbers 25:9 gives no time specification as to when the 24,000 deaths occurred from this plague. The passage in I Corinthians, however, does, specifically noting that 23,000 died in one day. The logical interpretation would be that the other 1,000 died the next day after the plague afflicted Israel, probably as the residuals of the epidemic among the people. This objection to the Bible would rightly be classified under the category "nit-picky non-issues". Only a critic who is completely willing to jettison a straight-forward logical reading of the texts would demand that this "has" to be an error in the Bible, and not rather a case of simple failure to read thoroughly on the part of the critic himself.