How to extract all possible sub-products which match specific pattern?

To get all the different ways this pattern can match, we can use ReplaceList, since none of Cases, Replace, ReplaceAll tries to match the same part more than once. Here is one way:

ReplaceList[expr, 
 d_. + Times[c___, Dot[a_, b_], f[x_]] :> Dot[a, b] f[x]]

{a.b f[x], c.d f[x], m.n f[y], p.q f[y], r.s f[y]}

The reason I'm writing Dot[a_, b_] and not just a_.b_ is that looking at the FullForm of what I'm trying to match always seems to help me figure out a good pattern to use :)

You can also use SequenceCases with the option Overlaps -> All:

SequenceCases[List @@ expr, { _.  a_Dot  b_f} :> a b, Overlaps -> All]

 {c.d f[x], a.b f[x], r.s f[y], p.q f[y], m.n f[y]}