If you really put index.html/ as the default root object and your CloudFront distribution is pointing to the web site hosting endpoint of the bucket and it worked, then you were almost certainly serving up an object in your bucket called index.html/ which would appear in your bucket as a folder, or an object named index.html inside a folder named index.html. The trailing slash doesn't belong new there. This might explain the strange behavior. But that also might be a typo in your question.
Importantly... one purpose of CloudFront is to minimize requests to the back-end and keep copies cached in locations that are geographically near where they are frequently requested. Updating an object in S3 isn't designed to update what CloudFront serves right away, unless you have configured it to do so. One way of doing this is to set (for example) Cache-Control: public, max-age=600 on the object metadata when you save it to S3. This would tell CloudFront never to serve up a cached copy of the object that it obtained from S3 longer than 600 seconds (10 minutes) ago. If you don't set this, CloudFront will not check back for 24 hours, by default (the "Default TTL").
http://docs.aws.amazon.com/AmazonCloudFront/latest/DeveloperGuide/Expiration.html
This only works in one direction -- it tells CloudFront how long it is permitted to retain a cached copy without checking for updates. It doesn't tell CloudFront that it must wait that long before checking. Objects that are requested infrequently might be released by CloudFront before their max-age expires. The next request fetches a fresh copy from S3.
If you need to wipe an object from CloudFront's cache right away, that's called a cache invalidation. These are billed $0.005 for each path (not each file) that you request be invalidated, but the first 1,000 per month per AWS account are billed at $0.00. You can invalidate all your files by requesting an invalidation for /*. This leaves S3 untouched but CloudFront discards anything it cached before the invalidation request.
The default root object is a legacy feature that is no longer generally needed since S3 introduced static web site hosting buckets. Before that -- and still, if you point CloudFront to the REST endpoint for the bucket -- someone hitting the root of your web site would see a listing of all your objects. Obviously, that's almost always undesirable, so the default root object allowed you to substitute a different page at the root of the site.
With static hosting in S3, you have index documents, which work in any "directory" on your site, making the CloudFront option -- which only works at the root of the site, not anywhere an index document is available. So it's relatively uncommon to use this feature, now.
