Here, you can see that the previous roof was left on the structure, and the newer roof was installed over the top. This type of installation is not recommended and frequently does cause problems. 

In these photos, you can see the portions of the facia board are broken, and the gutter is in poor condition and pulling away from the structure.  This could be responsible for most of the damaged soffit.

Take a look at how the shingles slope up over this hump. This causes water to dam and potentially weep between shingles through nail holes

In this photo, you can see the organic material gathering underneath the shingle. These shingles are no longer adhered to and are susceptible to wind damage.

In this photo, you can see that the ridge vent is old metal style. The fasteners have begun to come loose and are likely to cause small leaks. These should be repaired or replaced.