Okay, I have all the packages working, I think (will take some use to see if I find a glitch). The errors seem to be related to the directory structures not being set up in the package files. For example, if I try to go to the default settings for the Tag package via Preferences > Package Settings > Tag > Settings - Default, I get this error:
Unable to open /C/Users/Matt Tyree/AppData/Roaming/Sublime Text 3/Packages/Tag/Tag Package.sublime-settings
And it's not there because installing the package only creates the file under Installed Packages and the Tag folder is not created under Packages as it is in ST2. Nor is a user settings file created under the User folder.
The same happens with BracketHighlighter, DocBlockr, Emmet, Package Control, SideBarEnhancements, and SublimeOnSaveBuild (of the packages I have installed). However, PlainTasks and SFTP don't get the error because those packages DID create the folders.
Even Sublime default settings, Settings - Default and Key Bindings - Default, get the error because no Default folder is created.
HOWEVER, I notice that a file still comes up even though the error is displayed in the console. So, I guess it all works, just not very elegantly.
P.S. Where's the subscribe button for forum threads?