I’ve made so many mistakes that I can’t even count them all.
so much that you wouldn’t believe it/more than you would believe
「more ~ than I can count」とか「so many ~ that I can’t even count them all」と言う表現は「○○は、全部数えるなんて無理ほど多いよ」と言う意味です。「more than you would believe」の意味は同じぐらいですが、「誰も信じられないほど多いよ」と言う意味もあります。