The first, and easiest, thing to try would be to redirect from the old domain to the new one. You don't need to install the old site again to do that.
With most hosting set-ups you can "park" another domain over the main one. If you do that it will appear to work. However you also need to ensure that you have a 301 redirect in place. This is just one line added to an .htaccess file on the server. If your web guy doesn't know this stuff find someone who does to make sure it is in place and correct as it is vital (then start looking for a new web guy)
That will at least ensure that any link equity the old domain has is being passed to the new site. However it doesn't address whether the new site is as well optimised as the old one. The on page optimiser tools here on seomoz might be useful in checking that. It is quite simplistic though and it is only dealing with a page at a time rather than the overall site. However it might give you an indication as to whether you are likely to face problems with the on site stuff.
Hope that is some help.
Google doesn't actually have an issue with directories. It has an issue with links that have no value - which includes the vast majority of directories. Those that do count though are few and far between and it is now probably best to steer clear if you are not certain.