maybe writting tests for those possible bugs is also going overboard ?
There are two situations that your statement made me think of. In both, I'll argue in favor of writing the test.
The first case is some edge case that "will always be true...duh!". Dollars to donuts, something will change to break your assumption. At that point, you'll be glad that you had the test in place.
The second situation is a known bug that your customer has told you is acceptable. In this case, write the test, but set it to be ignored in your suite. That way, when some big wig walks up and says "did we know about this? the client is fumming!", you can say "yep, and here's the test case that Mary Jones told us to ignore on 17Nov2004".
Feel the white light, the light within
Be your own disciple, fan the sparks of will
For all of us waiting, your kingdom will come