Some issues you will run into are:
co-ordination of who tests what
determining who tests what parts of security
determining the feedback mechanisms for each
changes in one area that affect the other
standards for where validation is done (can be both)
Essentially the issues are mostly about
Communication and co-ordination
combining API and UI
Since a user story describes a feature and features could consist of UI and API changes, I guess this is pretty natural and happens all the time on different teams.
API and UI implementations and validation
Validations are something that usually have to be implemented, both on frontend (html, JS) and again on backend because we can't ...