Hi @Greenhorn,
Sorry for the trouble!
When you see the “Update Failed.” error, is there any other information? It might help to follow the steps in this FAQ: Help! My Local site cannot establish a connection to WordPress.org
The actual PHP error looks like it’s caused by the failing downloads like you said. To fix that, your best bet is to manually browse to the site’s app/public/wp-content folder by right-clicking on the site in Local’s sidebar and then going to “Show Site Folder”
Once you’re in the site folder, browse to the plugins and themes directories and remove the themes/plugins throwing the errors.