A website is a lot of moving parts, there is the design, then there is input from the UX/UI personnel, and then there is the content from the writers. All this needs to fit together into one seamless whole, and that is the objective of the designer. Here is a basic checklist from Rack Alley that will help narrow down some of the things that you will need to keep an eye on:
The first step is to make sure that someone with enough authority defines the goal of the website. The decision needs to be come from management, and that will form the basis of everything that goes into it. We want all the teams pulling in the same direction.
There is research that shows that it takes only 0.05 seconds for a visitor to make a judgment about a website. The first impression is critical, and do everything, including the use of images, text, headers, calls to action etc. that will keep your visitors around a little longer.
Surveys show that more than half of web traffic is now from mobile devices, making it critical that you have a mobile version of your site, and that it is as fully functional as the desktop version. Forcing a mobile user to seek a desktop to complete certain tasks is asking for trouble.
There are many other factors, list hosting at a Los Angeles data center, etc, but the above three should give you an idea of how to approach and create your own checklist.