The only problem, I think, occurs when you book two separate tickets as a connecting itinerary (eg. purchase HKG-LAX and separately purchase LAX-JFK, as a connecting flight). If your first flight is delayed, the airline may not take responsibility to get you to your final destination. Whenever I do this (for instance splitting DTW-FRA-DFW-DEN-DTW into a DTW-FRA-DTW ticket and a DTW-DFW-DEN-DTW ticket) I leave extra time for the connectin between tickets and If I get in on time, just get them to put me on an earlier flight.