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Hmm. Try making a video sitemap with a few videos that currently aren't appearing in serps, submit to GWT and see if they appear in a week.

Well as for the 404s, I would run the site through Screaming Frog and see what I get. If you find 404s there, then redirects and edits will be needed to fix them. Otherwise forget about the GWT report. I think the most important thing for you to do (besides an overall marketing campaign) is fix those duplicate page titles and descriptions. This is a huge factor, undoubtedly. A PPC campaign (executed properly) can always help, but you shouldn't lean on it as your fix to your marketing campaign. It is only another spoke in the wheel of your overall efforts. Hope this helps.

It's better to use 301 redirects to maintain the SEO value if possible. Redirect the blog post urls to a corresponding content page on your website if such content exists. It's better for the customer experience too. If the blog posts are about topics or events that our outdated, a custom error 404 page is a better option so that the visitor won't waste time looking for something that doesn't exist anywhere on your site, even in another format. Listing your sitemap or a search feature can be helpful.