A developers life can consist of new features, change requests and bugs.

The basic approach to bugs is to fix them in priority order.

A more sophisticated technique is to identify that cause of the bug, and introduce a change in the process to prevent it from happening again.

For example, if you are using mvc you may have a convention based set of images.
A simple powershell script can check that the images exist in the correct location from a simple list of pages.
This list could be hardcoded in the tests, but will probably be available from somewhere else in the system.

A similar approach can be taken with logs. It can be assumed at minimum that you are logging errors.

If you only look at the logs when you have a specific error then you are missing out on a lot of data.

Simple analysis of the logs data, such as obtaining counts of each of the types of errors within an hour, will provide massive benefits.
Firstly you will be able to find the most frequent errors – even if the users are not reporting them.
If the error is not a real problem, downgrade it to a warning. If it is a real problem then it should become a priority to resolve.
Secondly it will show you areas where there are missing errors, especially if the users are reporting errors that the logs do not show.