When searching for images, results are loaded in batches of 40 at a time. Currently it is very easy to hit rate limits on commons this way; see parent task (T258833) for details.
Introducing a lazy-loading behavior for images (and potentially other result types that have thumbnails, like videos) will hopefully mitigate this problem somewhat, and will also generally improve performance (both actual and perceived).
Should be visible on production Commons starting Wednesday, August 12.
This might not eliminate all 429 thumbnail errors, but it should greatly reduce them since images won't load until they enter the viewport. It is possible that rapid, aggressive scrolling to the bottom of the screen repeatedly may still cause the rate limit to be hit.