I realized that there was a mistake in the number of orders we have made.
I realized that we've made a mistake with our order.
ご質問ありがとうございます。
① "I realized that there was a mistake in the number of orders we have made."=「発注数に間違いがあったことを気が付きました。」
② "I realized that we've made a mistake with our order."=「注文内容で間違いをしたことに気が付きました。」
ご参考までに。