One SEO implication that redirecting all of your error 404s to the home page is that it could lead to Google and other search engines to flag your site for having 'soft 404 errors.'
Best practice is to have a custom 404 page, that returns a 404 message, that then helps the end user find what they are looking for. Either a list of top categories, a search box, or a phone # to call tech support.
Here's what Google says about why you shouldn't do this:
https://support.google.com/webmasters/answer/181708?hl=en
Returning a code other than 404 or 410 for a non-existent page (or redirecting users to another page, such as the homepage, instead of returning a 404) can be problematic. Firstly, it tells search engines that there’s a real page at that URL. As a result, that URL may be crawled and its content indexed. Because of the time Googlebot spends on non-existent pages, your unique URLs may not be discovered as quickly or visited as frequently and your site’s crawl coverage may be impacted (also, you probably don’t want your site to rank well for the search query [File not found]).
We recommend that you always return a 404 (Not found) or a 410 (Gone) response code in response to a request for a non-existing page. You can improve the user experience by configuring your site to display a custom 404 page when returning a 404 response code. For example, you could create a page containing a list of your most popular pages, or a link to your home page, or a feedback link. You can also use the Webmaster Tools Custom 404 widget to add a search box and more site search options to your site. But it’s important to remember that it’s not enough to just create a page that displays a 404 message. You also need to return the correct 404 or 410 HTTP response code.
