This is quite common practice, so no there's no issue with this whatsoever.
Typically dedicated DNS providers provide better performance than the DNS service domain registrars bundle with their service, so if it's performance in particular you're worried about, you'll probably find things faster using separate providers.
Edit: based on closetnoc's comments let me expand on this a bit. I should say that I work for a company that provides DNS services so I have some level of bias here.
An Anycast DNS service will usually give you better performance than a Unicast service, as well as better availability; particularly if your site has visitors from all over the world. In my experience, it's common for dedicated DNS providers to offer Anycast services, but it's unusual for a DNS service bundled with domain registration to be Anycast. So that's what I based my generalisation on. Since the question mentioned GoDaddy, they appear to have an Anycast service (their 'Premium DNS' product) for an additional monthly fee, so I assume their free service is Unicast, but I don't know this for a fact.
I agree with closetnoc that looking at providers on a case-by-case basis would be better, so if performance is a concern for you, test the providers you're considering (ideally from regions where your site visitors are likely to be) against your current DNS and use that info to help with your decision.