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If you are using similar tags for almost every post, yes it will create duplicate content, but If you are using them separately it wont create duplicate content.

For an example I had a movie site, I used tags for the Movie Cast, since every movie has different cast it never created any duplicate content, my that site was SEO miracle.

Duplicate content kills the ranking, I had been facing the issue due to the usage of Os Commerce, however, since I fixed the duplicate content my site ranking is getting better every day. The process is painfully slow but there is an improvement, Use Google webmaster tool to track duplicate title tags and content.

The categories you have deleted might be appearing as Page Not Found errors, this also effect search ranking as far as I know, you might see improvement in ranking in a few days.

Good Luck