His lies were so full of holes that no one believed them.
Tips
memory
破绽 literally means a 'split seam' on clothing - a tailor's term for a tear that gives away poor stitching. 百出 (a hundred coming forth) means flaws appear everywhere. Picture an argument like a torn shirt - holes popping open with every move.
usage
Most often used about lies, alibis, theories, or excuses - anything that can be 'unraveled' on inspection. Strong companions: 漏洞 (loophole), 站不住脚 (can't stand up).