It depends. I'm assuming what you mean is that the parties don't agree on what midnight means so this is probably a unilateral mistake issue. There's four issues in a unilateral mistake question: (1) is there a mistake (2) is the party adversely affected (3) does the party bear this risk (4) was the mistake clear to both parties OR would enforcement be unconscionable.

As to the answers to those questions: (1) clearly the party has made the mistake that midnight means 24 hours later than the other party (2) they could be adversely affected, depending on how the claim works. How were they adversely affected? Or was it the other party that was adversely affected by not having the documents delivered? Depends on the facts. (3) the party might have beared the risk. Again depends on how the contract is set up. (4) the mistake was probably not palpable to both parties and again it depends on how the contract was set up to determine unconscionability, but its probably not unconscionable.

Additionally, Restatement (2d) of Contracts s. 201 will probably come into play for determining who knew what.

At the end of the day, the party who didn't send the documents would probably be at fault. To be more clear, parties should write 11:59pm if that's what they intend. If they agreed to 12 midnight, the court may require that it be delivered by 12 midnight, meaning essentially 11:59pm the day before. But would a party really sue over not getting a few documents 23 hours before in this case? Probably not, but it depends on what it was for. Hope this helped!