Its highly unlikely that anything will happen to you for paying a day late. The worst thing to usually happen for unpaid fines is that they go to collections after they are a month or two late. The cops are not going to come looking for you. Just call the court on Monday to make sure its all paid off. The clerk would tell you if there was any problem with your late payment, but its highly unlikely they will care since you substantially complied.
You might have a late fee. Call the court clerk and check with them. As for a warrant and a possible probation violation; you can check with your probation officer if you are on supervised probation. Usually there is a lag in time from when a notification of unpaid fine is sent to probation and them doing anything about it. They will probably check to see if it has since been paid, which yours has. If you are not on probation it is a non-issue. Either way, being a few days late is unlikely to result in any warrant being issued. No promises here, but I have never seen it under the circumstances you described
I agree, it is typically not a problem to be a few days late with a payment, especially if it's the last payment. But I would call the court clerk's office and ask them if everything is OK, that will probably ease your mind.