I see on sites like Travelocity, you can book flights with two different airlines, the first leg, for example, on Frontier and the second leg, for example, on United. Is there any problem with booking a flight like this? Any potential problems?
They work the same as any other connecting flight. I would not do one myself unless it was a frontier / airtrain switch for legs since they are owned by the same company. I think the risk when using two totally different carriers is greatly increased and it will save you the hassle in the event one flight does not leave or arrive on schedule if you just pay a few extra bucks and fly the same carrier.
Don't forget that switching airlines often means switching terminals which could mean a loooonnnnnnggggg hike across the airport to get to your next flight. It's tough enough connecting on one airline sometimes. We had a 30 min connection with United in Denver, which has a long terminal. We came in at one end and were to depart at the other end. We made it, just. If we were to switch airlines, too... forget it.