In the early stages it is very important to monitor your site’s reputation using something like Google Alerts or even a paid solution.
Assuming your marketing strategy was a success your site should be receiving traffic and natural backlinks.
Respond to any major issues about your site/service on your company blog and answer comments with grace and transparency on any other blogs.
If somebody writes about you then it might be an idea to thank them or remember them for the future.
Analyse your stats to see where your valuable customers came from and see if you can improve the traffic from those sites.
One important strategy is to analyse how your site is being indexed by Google. Check which pages are being spidered and which are being indexed and make sure you fix any 404 errors or broken links.
The most important thing is to take user feedback into account and use it to improve your site, if somebody spots an error then try to get it fixed as soon as possible.