Temptation To Overbuild
Many web designers tend to get carried away. Too
many moving elements, too many fonts or too much
content can do more harm than good. It is important
to recognize the importance of white space and
achieve a balance between all the visual elements of a
website. Showcasing all the skills in one website
might be tempting but it might just be too
overwhelming to the visitors.

Ignoring Cross Browser Compatibility
A common mistake many web designers make is to
assume that once the design process is completed
and the content is uploaded, their job is done. While
HTML, CSS, and JavaScript coding might be the same,
different browsers especially the older ones such as IE
6 & 7 often interpret the code differently resulting in
an undesirable display. Responsible web designing
requires that the website be tested across multiple
browsers before launch.

Not Testing For Mobile Compatibility
With the increasing popularity of smart phones and
tablets, web designers face new challenges. Websites
need to be tested for different screen resolutions.
Also, using Adobe Flash on a website can create
complications for mobile viewing on devices such as
iPods and iPhones. Addressing these issues with
clients beforehand can save a lot of time and effort.

Source: http://www.arewatech.com/2013/01/web-design-mistakes-you-should-avoid.html