The criteria for inclusion in the CRSP index specify "a minimum total market capitalization of more than $10 million with a float that more than 10 percent of the total shares outstanding". So there is sub-micro stuff 'beneath' the index that's not included due to the $10M minimum, and others that aren't included because of the float requirement. Do you care? Probably not, but you might.
Also, I've periodically heard arguments against market-cap weighting, which is what indexes do (this is probably one of those "downsides of indexing" arguments). If you are not careful, with a couple of index funds you can end up really exposed to a handful of very large, and therefore highly-weighted, blue chips. But I can't think of another way of weighting within a whole-market index that would make sense.
The other thing that comes up a lot, mostly in tech circles, is that index funds (of course) don't give you exposure to the private market, and it seems that more and more tech companies are waiting a long time until they go public, such that at any given time a lot of growth is happening where most investors can't get in on it. The argument is that, if you are financially qualified, there are more opportunities out there for qualified/accredited investors on the private market. I don't personally agree with this if you're looking for an investment rather than a job as an investor, but you'll sometimes hear the argument get made.
If the total market is outperforming S&P 500, that means the companies not in S&P 500 perform better overall, so giving them greater weight than suggested by their relative market cap would have been beneficial.