The Lord always keeps his promises; he is gracious in all he does. The Lord helps the fallen and lifts those bent beneath their loads. The eyes of all look to you in hope; you give them their food as they need it. When you open your hand, you satisfy the hunger and thirst of every living thing. The Lord is righteous in everything he does; he is filled with kindness. The Lord is close to all who call on him, yes, to all who call on him in truth. He grants the desires of those who fear him; he hears their cries for help and rescues them. (Psalm 145:13-19 NLT)
God might build upon our mistakes in ways we don't immediately see, though. It might take us some time to begin to see how he takes parts of those broken down places of our lives we label as "mistakes" and uses some of what others see as "rubble in those ruins" to bring something of monumental beauty in our lives. Not all that comes from our mistakes should be discarded and unused. In his hands of grace, those things others may label as "rubble" can become the most majestic of building blocks for something of even greater beauty and deeper strength than we ever imagined possible. I think this is what our psalmist may have in mind when he refers to God opening his hand and satisfying the hunger and thirst of every living thing. Mistakes leave us hungering - thirsting for God's grace. In his kindness, he uses those opportunities to grow us - we want to beat ourselves down - but he wants to build us up even when all we can offer to him is rubble.
Hiding mistakes never gets us anywhere. We can try as we might, but God knows those mistakes exist. He also is the only one totally able to pick out the pieces of those mistakes that will make the foundation of growth that ensures repeated failure will not occur. I think we try to manage our mistakes on our own, either because in our pride we are not willing to admit our wrongs to anyone (even God), or because if we admit them, we might actually have to assume some responsibility for them. Either way, God is kept out of the potential recovery from those mistakes until we humble ourselves enough to admit them, or we own up to them and acknowledge we had a part to play in the outcomes we are seeing.
While it may be hard to see mistakes as ground upon which miracles can take form, I think it is quite possible God's greatest works in our lives are done not in the absence of mistakes, but because of them! Just sayin!