It depends on what you mean by overlook. There are so many kinds
of programming languages and each does different things.
Since you said it's a website, I assume it's related to SQL?
Does the website has some kind of DB? What kind of programming
language is used to query the DB?
Most use PHP to query the data in MySQL. SQL queries, if not
properly sanitized, can result in an attacker doing all sorts of
things to the DB and the website.
Also, how does the company's network layout look like? Where the
servers located? Public? De-militarized zone?
Lastly, have all the web pages been checked? There's been a
recent spate of SQL injections done via JavaScripts. Sometimes, a
website can get attacked without them knowing. If any attacker
chances upon the website, he can abuse that info.
Here's one example - http://securitylabs.websense.com/content/Blogs/3053.aspx
If your company is big enough, they should hire pen testers to
test the site. Pen testers is short for Penetration Testers. They
are a group of hackers which are paid to hack. They have the
permission of the management to break into things. Once they done
their work, they'll have a report for the company and some
recommendations on how to resolve the security issues.
Alternatively, you can use automatic tools to find errors in the
website and fix them if the company has got no money to hire such
testers.