Does Salesforce have a list of all the exceptions published somewhere on the web?
Somewhat and no. Most are published by the API that uses them. If you want Apex exceptions, you can find them in the Apex Code Developer’s Guide. Others (like SOAP and REST), you’ll find in the API documents for the particular API linked from the Developer Documentation page. There are some, that simply aren’t documented and you’ll typically receive a message that will appear along side of them to contact Salesforce Support for more information.