In the Salesforce Error Dashboard, you can see all of your Salesforce errors - both trigger and activity/data sync errors. You now have the power to retry one or many failures and can see in the dashboard if they were successful and if not, the reason why.
Here is a list of common errors.
To find the dashboard go to the Integrations tab then click on Salesforce's tab "View Integrations" 
The Sync Errors tab is where you will see any activity/data sync failure. It will tell you the reason for the error as well. Use the common errors article for more information about your specific error.
You can see all of your triggered sends under the Trigger Logs tab. This will show you how many have been successful, and it will also advise if there has been an error with the trigger. 
If there are any failed sends, you can click on Trigger Logs to retry. Here you can see which ones failed and you have the option to Retry All Failures or select the checkbox for retrying specific failures.
Reach out to your CS resource with any questions or check out the error list here on how to use the dashboard!