The age of the home is not the problem, but to answer your question, here is a list of some of the "potential traps":
Condition: Have a good home inspection performed to check the condition of all systems including the roof, heating, air condtitioning, plumbing, gas plumbing, water heater, electrical, structure, etc.
Asbestos: Used a lot in older homes as it was a sort of miracle material, lightweight, insulating, easily manipulated. It is in flooring, wall plaster (king's coat), pipe insulation, heating and water heater vent pipes, and most home inspectors will point it out for you.
Galvanized steel water pipes; Corrode from the inside, and if they haven't been upgraded to copper or pex pipes, will cause restricted flow and leaks.
Old cast iron drain pipes: when buried, will corrode from the outside, and video scoping the inside of the sewer lateral line will not detect this. If the sewer lateral line has not been replaced with PVC or ABS pipes, the replacement of such will be expensive. If you have clay pipes buried, they need to be upgraded due to the age of the pipes also.
Electric wiring: Knob & Tube wiring used in the 1930's and 40's is considered dangerous and should be upgraded if present. Most insurance companies will not insure this type of wiring.
Aluminum wiring used in the 1960's and 70's is know to cause fires when connections fail or are improperly connected. UL listed connectors can be installed at every connection to minimize the risk, but connections are often overlooked by electricians, and it is expensive to do this retrofit correctly. It may be better to re-wire the house with copper wiring.
Electric outlets: May have old style "2-prong" outlets, or worse, 2-prongs may have been replaced with 3-prong outlets but without connecting ground wire. The 3rd prong is for grounding which is needed for safe operation of any appliance which has a 3-prong plug, and the grounded outlet is needed for surge protectors to properly protect electronics and computers. If the ground wires are present at the outlets, upgrading the outlets is not too expensive, but if the ground wire needs to be run to every outlet, it gets very expensive.
These are problems associated with older houses only. New houses have their problems also, such as Chinese drywall, and polybutylene water pipes. This is a partial list, but represents some of the more expensive concerns, health concerns and safety concerns.
A thorough home inspector will point these problems out to you, and let you know if the house has been upgraded in each of these areas. Be careful that you choose a home inspector working on your behalf who will report these problems honestly. If the inspector relys on agents' referals, or gets paid at closing, they have an interest in the deal going through without hitches, and might overlook some concerns.
Check out these websites for more information about choosing a home inspector: