Short Answer
The contractor should consider threshold, sill, flashing, framing, weather-resistive barrier, trim, sealants, siding, and drainage.
Detailed Explanation
A door replacement isn't just about the door — it's about the entire opening assembly. The contractor should evaluate: the threshold and sill condition (is there rot or damage?), the flashing (is it present, properly installed, and integrated with the weather-resistive barrier?), the framing (is the rough opening structurally sound?), the weather-resistive barrier (is it properly installed and integrated with the door flashing?), the trim (is it in good condition and properly flashed?), the sealants (are they intact or deteriorated?), the siding (is it properly integrated with the door opening?), and the drainage (is water directed away from the threshold?). Evaluating all of these components ensures the new door performs properly and doesn't just cover up existing problems.
Why It Matters
Evaluating the entire door opening — not just the door — prevents installing a new door over hidden problems that will cause it to fail.