The crawler could not communicate with the server. Check that the server is available and that the firewall access is configured correctly.

Unable to access object.

SharePoint 2010

Broke my content sources out by Site Collection. After doing this, my crawls would take a LONG time or I would see thousands of errors like the ones above.

In IE, I signed into SharePoint using the default content access account that the SSA uses to crawl content. When I navigated to the Site Collection that was error-ing out, I could not open any of the site page(s) or content.

Steps I followed to fix the issue.
Using my personal account, I opened the Site Collection.
In the top right corner of the browser I clicked on my name, then selected Sign in a Different User.
Signed in using the crawl account (default content access account).
Then reloaded the page. It took several tries before the page would load.

Once the page(s) started loading, the crawler was able to crawl the site(s).