It is a big deal for a couple of reasons:

1. Improperly formatted HTML is significantly harder for search engine bots to navigate, meaning that Google might not be able to accurately gauge the content of your site.

2. Improperly formatted HTML is more likely to mess up in different browsers; for example it may work in Firefox but not Internet Explorer.

I suggest you have it fixed by someone with some HTML knowledge. They will make sure your Amazon affiliate links come out unscathed.

I am actually a programmer myself, so if you're interested in having me do it, feel free to PM me. But no matter who you have do it, you should definitely fix these errors.