"Automated tests should find bugs" or "find more bugs" is a very common misconception. Basically this says that finding bugs is a valid objective for automation. I don't agree - I think this is generally a very poor objective for test automation. The reasons are to do with the nature of testing and of automation.
Testing is an indirect activity, not a direct one. We don't just "do testing", we "test something". (Testing is like a transitive verb which requires an object to be grammatically correct.) This is why the quality of the software we test has a large impact on testing: if a project is delayed because testing finds lots of bugs, we shouldn't blame the testing! (I hope that most people realize this by now, but do have my doubts at times!) Testing is not responsible for the bugs inserted into software any more than the sun is responsible for creating dust in the air. Testing is a way of assessing the software, whatever the quality of that software is.
Test automation is doubly indirect. We don't "do automation", we "automate tests that test something".
Automation is a mechanism for executing tests, whatever the quality of those tests are (that assess the software, whatever the quality of that software is).
Bugs are found by tests, not by automation.
It is just as unfair to hold automation responsible for the quality of the test, as it is to hold the testing responsible for the quality of the software.
This is why "finding bugs" is not a good objective for test automation. But there are a couple more points to make.
Most people automate regression tests. Regression tests by their nature are tests that have been run before and are run many times. The most likely time a test will find a bug is the first time it is run, so regression tests are less likely to find bugs than say exploratory tests. In addition the same test run for a second time (and more) is even less likely to find a bug. Hence the main purpose of regression tests (whether automated or not) is to give confidence that what worked before is still working (to the extent that the tests cover the application).
Of course, this is complicated by the fact that because automated tests can be run more often, they do sometimes find bugs that wouldn't have been found otherwise. But even this is not because those tests are automated, it is because they were run. If the tests that are automated had been run manually, then those manual tests would have found the bugs. So even this bug-finding is a characteristic of the tests, not of the automation.
So should your goal for automation be to find bugs? No! At least not if you are planning to automate your existing regression tests.
I have been wondering if there may be two exceptions: Model-Based Testing (where tests are generated from a model), and mature Keyword-driven automation, i.e. using a Domain Specific Test Language. In both cases, the first time a test is run is in its automated form.
But hang on, this means that again it is the tests that are finding the bugs, not the fact that those tests are automated!
"Finding bugs" is a great objective for testing - but it is not a good objective for automation.