You will need to make sure you are not violating the other website owners intellectual property. Off the top of my head I can think of several issues:
1. Copyright - if you are copying any code directly than that may be a violation of copyright law.
2. Look and feel - if you are copying the look and appearance you may be violating their trademark and/or trade dress
3. If you are using any methods which they coded into their site you may be violating their ideas and patent rights.
For all of these reasons I would not recommend this unless you have a very good attorney willing to write you a freedom to operate later stating he/she has reviewed all of these issues and does not believe you are violation of IP rights.
Registered USPTO patent agent with 11+ years of patent filing experience. Filed over 500 patent applicaiton in many technology areas. Check out my website: http://patentfile.org