You should pay attention to any language in the agreement that in so many words suggests that your investors have the right to walk into your office and tell you how to do your job, who to hire, how to develop and market your product, how to design your website, etc. After all, no CEO enjoys this type of “oversight” that will likely stifle his ability to move his company in the desired direction as soon as possible.
Of course, if your investors are not simply passive third parties but your parent company, or a company that is in the same industry as you are, they will likely want to have significantly more involvement in the key aspects of your operations, such as product development, sales strategy, advertising, etc… In this case, the terms of this broader involvement should be carefully analyzed and negotiated to avoid future disputes over who is in charge of what and why. The more specifically you outline what your investors can and cannot do, the lower the chances will be of any dispute with them that can lead to all kinds of problems, including interruption in funding and lawsuits.