To me it sounds fine and indeed it sounds pretty much the same as
Dinner was the next problem (it's almost as though you were making a list of all your problems and dinner was next on your list)
However if you say
(Now/well), dinner was another problem.
to me this sentence could also mean I had a totally different problem to the one I had been dealing with e.g.
(Well, dinner) was another/a different problem. The most important thing now was to get him to the airport on time.
I hope I've come up with the right example and that I haven't confused you any further.