This error below addressed in security patches but still outstanding in the latest version of Magento 1
The following is relevant if you have applied SUPEE-10570 (VERSION 1) or are using a Magento version that includes SUPEE-10570 (VERSION 1). Please note that Magento issued a fix for SUPEE-10570 and SUPEE-10570 VERSION 2 fixed that issue. If you are using SUPEE-10570 VERSION 2 you do not need a code change and can ignore the following. The issue can be replicated when "required registration" is enabled. Symptom: when placing a successful order for new customers, you are redirected to the homepage instead of redirecting to the order success page. The order is saved, but the customer is not logged in.
Solved! Go to Solution.
So, basically, the recomendation must be to apply the SUPEE-10570 V2.
There were some issues with checkout when version 1 was applied but version 2 has fixed those issues.