Well, further analysis with more data may be needed, but, at first sight, it seems that the only problem you may have is a malicious user exploiting the program behind the socket, gains the same privileges as the program and may gain root access depending on the environment.
Apart from this I can't see any other problem. But consider making this exercise:
- Has been the software properly tested and audited regarding security topics?
- Can your program damage any other process if it gets hacked?
- How much access do you concede an user if your program gets hacked?
- Is there any critical information in the same user space?
- Is there any other way to launch the program who attends the socket less risky? Is it worth?