He should have kept the same URL structure and/or made appropriate 301 redirects where necessary. That is the biggest thing people generally screw up with this sort of thing.

"Our" ?

You don't have a webmaster or web developer. You have an idiot.

You should think about SEO before such a ridiculous move.

Now in case you don't know, wp and any cms puts things together,
and spits out html. Very easy to leave html pages alone. Duplicate
content is not an issue.

Hire a real web developer.

Paul

Definitely make sure he was on top of the 301 redirects. Be sure your site is signed up for google webmaster tools so you can see any crawl errors and be on top of them.

Another thing I often do for clients when they are getting a new site is provide a customized 404 page. This page often gives the visitor a coupon or free gift, so they don't feel betrayed for the broken link. You can spend hours and still not get all of the redirects, this is a good failsafe!

-Chris

SEO with Wordpress is the same as SEO with any other site-building mechanic.

Lucky for you, Wordpress has many free plugins which can make it easy to implement SEO techniques.

Did you have good rankings before the site was changed? If so, then SEO should have been looked at closely before anything was switched to a new platform. The good news is it's not too late to fix things usually and restore previous rankings, if you had them in the first place. If you didn't, then you shouldn't be too concerned and most likely the WordPress platform will give better SEO benefits than an older HTML site would due to the way WordPress structures things with multiple links leading to the same page (categories, tags, menus, etc).

1) You should check SEMRush to see how your rankings have been affected.

2) Install an SEO plugin, such as Yoast or All in One SEO Pack.

3) Be sure to configure the SEO plugin and actually use the extra fields it gives you on your posts and pages.

4) IMPORTANT: If you had good rankings before and they have dropped (temporary drop is normal, but should return before long), then have your developer ensure that the new pages have the same content as the old pages did. And of course, any URL changes should have the proper 301 redirects in place if they previously had any backlinks pointing to them.

5) Consider using a 301 redirect to your homepage instead of a 404 not found page, since this will send any backlink juice to your homepage instead of a 404 page if there are any backlinks out there pointing to URLs that no longer exist and don't already have 301 redirects in place.

That should cover the basics at least. Google is mostly interested in the content of your pages and doesn't care much about cosmetic changes, so as long as your main content has not changed and nothing else is seriously wrong, then your rankings should not get hurt much and will most likely improve if WordPress uses better structure than your old site did.

Hope that helps!

how many pages you have?
htaccess 301 redirect old pages to new.