The short answer is that yes, 2000s Mustangs are generally reliable cars. However, as with any vehicle, there can be exceptions to this rule. Some individual Mustangs may have been manufactured with defects that make them less reliable than others. In addition, the way a Mustang is cared for and driven can also affect its reliability.
For example, if a Mustang is regularly driven hard and not given proper maintenance, it is likely to experience more mechanical problems than one that is driven more gently and consistently serviced. That being said, even with proper care, any car can develop issues over time - so no vehicle is ever 100% reliable.
If you're considering purchasing a 2000s Mustang (or any used car), be sure to have it inspected by a qualified mechanic before making your decision. This will give you the best idea of whether or not the particular vehicle you're looking at is likely to be a reliable ride.