Hi Lana,
I've been having the same problem on one of our websites. I've been 301 redirecting over 5,000 URL's but still receive a lot of 404 errors. One of the main reasons for these 404 errors still appearing is other bots such as Bing Bot that is still crawling the old URL's.
To resolve this, I would just block them in your robots.txt file. We blocked our old product URL's that were under a "product directory like this:
User-agent: *
Disallow: /product/