HTML entities ensure your page is displayed correctly
As we have already mentioned, some characters like the ampersand (&) or the end quote (') are reserved for coding works. They are parts of your code. So, if you use them in the text of your body as well, search engines and browsers may sometimes fail to distinguish where they are parts of the code and where the are meant as a part of your text. For example, if you write:
Go to <a href='http://www.johnsbook.com?chapterID=1&pageID=15'>Chapter 1, page 15 of John's book</a> & check the third footnote.
Sometimes, this can be confusing to crawlers, as they cannot distinguish between the apostrophe that ends the value of the href attribution in the anchor tag on one hand, and on the other hand, the apostrophe after John. Another such confusion can occur for the ampersand which means and before the word check and is a part of the URL syntax in the anchor tag. The result will be an incorrect, often messy rendering of your webpage. Imagine if your readers see some messy codes instead of the article they were looking for, what will be their reaction? Letting your bounce and exit rates increase is never a good SEO tactics.
For the same reason, it is very essential to make use of HTML entities for SEO purpose particularly in the title and the meta description. Since these are the things that come up in the SERP (Search Engine Results Page), you must make sure your intended text is correctly rendered in all browsers under all circumstances.
Having a better architecture never hurts
If you do not use HTML entities, especially for the reserved characters like the end quote or the ampersand, you are going to get lots validation errors. While it is not too important for SEO, HTML entities can render your page passed in a code validation and thereby improve your page architecture. Having a good page architecture, after all, never hurts!
Passed validation check using HTML entities. And, SEO score has improved!
Yes, if you check your SEO score with sites like Nibbler, you are going to score low for being a W3C rebel. On the other hand, if you are W3C compliant, you can really boast about that (much like Google PR!) in the industry. Especially, if you are blogging about SEO tips or HTML coding, you should have as less W3C errors as possible (yes, you caught me, my page does have few W3 errors...hmm...looks like it's time to correct them!). While such use of HTML entities may not have direct impacts on SEO, it can really come handy for marketing purpose when you can show your higher SEO scoring, W3C compliant website to your advertisement providers!
A good reason for using HTML entities for SEO
If you are into blogging or search engine optimization, you must have gone through the blog of Matt Cutts a few times. And I think you will accept the fact that he is a lot smarter than us all! When I found him using HTML entities in his blog, I knew there is a reason for sure. Matt Cutts is not going to do anything unnecessary for sure, if there is not link between HTML entities and SEO, right?
A good reason for not using HTML entities for SEO
If you validate the great Google itself, you will find that it has lots of W3C errors. We can safely conclude, therefore, that HTML entities are not quintessential for SEO.
Conclusion:: Should you use HTML entities for SEO?
I think you should, even if HTML entities have no direct impact on SEO. Having HTML entities never harms, and who knows, there might be some advantage as well. However, since it is not quintessential, do not waste all your time putting the codes alone. Writing a great content, and writing regularly, is far more important to develop a great website over time. If you have some spare time (when you cannot think of a new topic to write on, or perhaps you have too less time to type an article), you can always go for tweaking your HTML entities. It never harms, I repeat!
More articles: HTML and SEO
Good article, a good webtool for html entities: http://www.html-entities.org/