If you run the SharePoint 2010 report viewer web part, you have probably already created a new permission level with limited rights to view the report. However, you may notice that the "Edit Items" permission level is required to render your report. This is obviously a problem because if your users have this permission, they can change the layout of this page, which is bad. What the regular user will see is the "Edit Page" option as a part of the Site Actions menu. This is the problem we're going to solve.
To get around this, you need to go your report library where your report is located. Hit the drop down menu next to your report and you should see "Publish Major Version." As soon as you do this, you can go back to your "Report Viewer" permission level (or whatever name you gave it) and remove the Edit Items level. When you revisit your page you will see that the report will run, and the user can no longer edit the web page.