Like any business acquisition it's not always what your buying that needs to be evaluated the most but you yourself and your skills. When it's internet related I would say it has a completely different set of problems than a typical service business has. Here are just a few things you may want to consider:
1) Are you versed in handling the daily operations of a website?
2) Does this website require one or more full time staff to run?
3) If a small income generator are you prepared to fix the site when server problems exist, code changes, bug fixes and general website maintenance?
4) What platform or code is the website built. Is it an outdated PHP, hard to find personal for Perl or is it WordPress based etc?
5) Does this website or it's contents infringe upon any copyright violations?
7) Has the domain name been banned or are there any alerts by virus scanning companies due to 3rd party links?
8) Is traffic bought or organic?
The questions related to purchasing any business could be countless. Many times you have to dive into a situation and take a leap of faith. I'd say the biggest things that plague website owners is getting code work done since there are so many code languages and people have different ways of solving problems. You can have ten people give you ten different answers on how to solve a problems and some of the problems related to a website are ongoing especially if it was not built proper code. If you understand code and can write your own code then you have an advantage. If not this could be your biggest challenge moving forward after purchase. Good luck!