Your templates contain code that generate HTML <form> tags, and those need to have special parameters and fields added in order to work safely on the internet. In v150 there were things added to ensure the proper safety. But if your upgrade skipped those things either in the default template files or your custom template files didn't get upgraded thoroughly, or if you installed addons that use old code from old addons designed for older versions, then any of those could cause the symptoms you describe.
I'd start by comparing all your /includes/modules/ and all /includes/functions/ files with original Zen Cart files. Then compare all /includes/templates/template_default files with originals. Then compare all your /includes/templates/YOUR_TEMPLATE_NAME/ against template_default versions of the same.
If that's not enough, do a complete comparison: http://www.zen-cart.com/wiki/index.php/Troubleshoot_-_Diagnosing_Obscure_Issues
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