Is tungsten a good metal for jet engines, besides the weight penalty?
No, tungsten would generally not be a good choice for jet engines.

Some of the parts that would need to be the most heat resistant, such as turbine blades are subjected to rotational forces that increase directly with the mass of the part. Thus a high mass material such as tungsten would increase the forces the part would have to withstand. These forces are already measured in tons per blade.

If you discount the high-mass quality of Tungsten, the biggest problem is that Tungsten is also brittle. If a turbine blade failed, as does happen, it would be very difficult to contain. Tungsten is used in armor piercing projectiles; the results of a tungsten turbine blade failure would not be good.