We have recently migrated our website and a lot of pages that existed on the old website no longer exist on the new website. We did create redirect rules to match the URLs from the old and the new website with a 301 but only for 50% of our content. We have around 195K pages which give a 404, and 180K pages properly redirected. We know serving a 404 to search engine bots is bad for PageRank, but are wondering whether it's bad for the overall ranking of the website. Here are our questions:
Q1: Is a 404 on a particular page affecting the PageRank of other pages and/or overall ranking of a website?
We know we can remove the 404 pages from the Google index via the webmaster tools but given the number of URLs that were and were not properly rewritten, we don't think we will be able to remove only the 404. We also know that eventually Google will remove those 404 pages of its index.
Q2: Is it better to remove everything and let Google re-index the website from scratch (and only non-404 will remain), or leave everything and have the 404 pages removed over time by themselves?