How to add a report an error button in a Drupal 7 website and collect user's browser details?
You could check out the Feedback module to see if it meets your needs - it's pretty simple and lightweight. If you don't want to use a contrib module, you could do something similar to the Feedback module - create a block (either using existing blocks in your theme or create a new block region programmatically), position it absolutely, and then link the 'Report an Error' block text to some kind of web form where you can collect the desired information. You could also use the Webform module to help you quickly create a form.