Google doesn't see itself as the W3C police – it wants to give users the pages that are most relevant and helpful for what they are looking for. Whether a page validates or not doesn't generally have an impact on whether a page is relevant or helpful, and so it isn't considered as a factor in Google's algorithm. But ... Google uses one HTML parser, and your visitors will use a variety of others. Any validation errors in your code might cause any one of these to get confused or throw a tantrum, and while most errors are pretty harmless, you don't want to run the risk of Google trying to read/understand your page and failing because the code is such a mess. It's always worth checking that your code validates, and fixing any errors that you can, because then you minimise the risk of something going wrong ... and if you do subsequently find a problem on your page, it's much easier to put it right if the validator isn't spitting back a long list of 200 other trivial errors that are nothing to do with it!
But no, minor errors that don't stop Googlebot from parsing your page won't have any impact on your position in the search results.