For "big issue not developed by you" it is not up to you personally to figure out how to handle this issue, so it automatically implies you need to bring it up with your immediate superior, along with an initial estimate of the severeness of the issue.
If at all possible up front also a suggested way to fix it - preferably also with an estimate.
The reason for this is that "big issues" may result in quite a bit of work to fix, and perhaps even cause schedules to slip if you need to redo a lot of testing etc. Hence it may well be declared a "known issue" to the users and not fixed yet, to keep on schedule.
But to reiterate, bring the issue to the attention of your organization.
EDIT: Also, coorporate culture should encourage that code is not owned by an individual but everybody. This means that it is not a blame game, but a common responsibility to find and fix. If somebody consistently produce sub-standard code, it is time to introduce code review to catch as much as possible as early as possible.