The opposite of the phrase "most well-constructed" would be "least well-constructed." This refers to something that has poor or substandard construction, which can make it unstable or unsafe to use. Other antonyms that may be used to describe something that is not well-constructed include poorly made, shoddy, inferior, and badly built. Such things are often characterized by low quality materials, poor craftsmanship, and lack of attention to detail. The opposite of "most well-constructed" often denotes something that is not durable, reliable, or aesthetically pleasing, and may fail to serve its intended purpose effectively.