You could try an incentives based approach to drive them to use the visual report. You could ask your tableau server admin to provide you with a view that shows the usage of your report by user. Then you could reward the users who were using it the most and resolving the most exceptions.
I would suggest to be most effective, you may want multiple 'data hygiene' type reports that just target specific areas eg product errors that product managers care about, financial errors that your finance guys care about.
They don't need to be overly visual - if there's data in the report, then there's an issue and if you're looking for a call to action, the most useful thing to see is what the issue is (ie the detail).
I have created several hygiene reports and there are people in the business who care about the data being clean to ensure their reporting is accurate, so they subscribe to the reports (as do I) and deal with issues if they're presented. By subscribing they get an email daily and if it shows no issue, its simply deleted; if there's data then the report is accessed from the email and further details understood.
If your users care about the accuracy of the data they're reporting, then they should care enough to want to be alerted to errors in the data, so should be happy to subscribe. In Tableau 10 you will have the ability to subscribe others to reports.
Here's a couple of examples of data hygiene reports I use
The above lands in my inbox daily, if there's a red cross in any of the tables I know the data is out of date and I alert someone to investigate, otherwise I just delete.
I use the below to keep an eye on who has a Desktop Licence that is now leaving so I can arrange to get the licence deactivated before they go so it can be reused with no issue. Its just a list - today it's empty so again I just delete the mail, otherwise it'll just have a list of names.