Changing to a dedicated server if definitely a good thing. A temporary drop shouldn’t go for more than 3-5 days, if at all.
What may have happened is that Google hit you site and saw the new IP and decided to run a deep crawl and re-value the content, the backlink value or other elements that their algo checks.
Any pages or information on another server will not be an issue as the domain name directs the bot.
Adding load of new content written for existing keyword targeting may be confusing the bots or causing them to lower the value or split the value between the old and the new pages, which would reduce your ranking. Its tough to say without looking at the site.
To be safe, run Xenu link sleuth and check for broken links and make sure you don’t have any 302’s, create an xml sitemap and manually submit it through google webmaster central, and also place the code (if possible) to verify the site is yours and check it the next day to see if you have any errors on the site.
Monitor the cache dates to see what the last snapshot was taken of the site/pages that are targeting the terms that are losing their rankings. If this date was before the drop, then the above tips will resolve the issue.