I wouldn't say that you're getting penalized--you're just missing out of all of the potential traffic to your site by not having your title tags optimized.
Yes, duplicate content is never really a good thing--best option for you at this time is to decide on where the content should reside and use robots.txt and Google Webmaster Tools to make sure the duplicates aren't being indexed.
From SEO point of view duplicate content is bad and it may hurt your rankings. You said that you have same titles on various pages which means that you are targeting same keywords on various pages which could cause the competition between the various webpages of the your site for rankings. Try to use different titles and remove the duplicate content for high search engine visibility.