What is the critical problem people face with a Web design and development agency?

Easy to answer. Most of them are useless. All they can do is compose poor quality Wordpress sites using page builders. Ask for anything bespoke or complex and they are unable to deliver.

Mostly people will face the issue of client co-coordination and  the in puts from the client. Apart from the design aspects or functionality issues these are the basic issues that web design and development agency will face.

if the client gives proper feedback and inputs it will be to easy to finish off the project in scheduled days before the dead line.