According to the release notes, the only known issue as of today is:
You currently cannot upgrade to this version using Magento Connect
Manager. We expect to resolve this issue soon.
Here's the list of changes directly from the release notes: http://devdocs.magento.com/guides/m1x/ce19-ee114/ce1.9_release-notes.html#ce19-1931
Bug fixes:
- We restored the old tax calculation algorithm for shipping charges. The patch to apply new calculation will be available on request.
- Resolved an issue with setting the session lifetime to 0.
- The monthly cron job that cleans up the table that contains IP addresses and passwords runs properly.
- All configurable product images are imported.
- You no longer get an exception due to an undefined addCrumbs() method call.
- Resolved the error Notice: Undefined index: session_expire_timestamp when accessing the storefront.
- Values for drop-down label values are saved correctly.
- The "Price as configured" for bundle products displays correctly in the shopping cart.
- Auto-generated passwords are sent to new customers as expected.
- The method Mage_Api_Model_Server_Handler_Abstract::processingMethodResult()
accepts scalar and array values.
- The default MySQL Full-Text search works as expected; it no longer returns all products.
- Catalog price rules return the correct price. Indexers now update all products instead of skipping the last product updated.
Security improvements:
- Prevented a potential Cross-Site Request Forgery (CSRF) vulnerability by changing the form key when a customer signs out of
the storefront.
- Prevented a potential Cross-Site Scripting (XSS) vulnerability when adding a category.
After checking it seems like there is only one security improvement in 1.9.3.1 that you can find here: https://gist.github.com/digitalpianism/9750b55c021832514a25c92695d735d9 . Please note that this fix is not included in any security patch as of today. #2 in the list above seems to be a wrong copy/paste as a similar line was already in 1.9.3.0 release notes
So there's no known backward incompatible changes between 1.9.3.0 and 1.9.3.1 BUT there is a backward incompatible change between 1.9.3 and 1.9.2.4 you can find details here: https://magento.stackexchange.com/a/142013/2380
And yeah it's totally safe to upgrade directly from 1.9.2.4