Many times, a roof leak is due to improper flashing. Another reason for
a leak (in the case of modified bitumen), is the failure to weld the
seams together. For the leaks to show up on your ceilings, it might be
the fact that you have both: areas where water is pooling, faulty
seams. If you do not have adequate slope for drainage, a portion of
your roof will have to be re-done to build up a slope to a drain.

In the case of a minor leak around flashings, all qualified roofers
should be able to spot the area where water is getting in. Roofing
compound with a UV top-coat is a pretty good fix that can last you a
couple of years.

In the case of a re-roof, you should opt for a hot-mopped (tar) roof
with a cap sheet (preferably granulated) roof. It's cheap (though they
might charge more for labor) and it lasts a lifetime. Roofers hate it.

-Vic