Selecting elements of a list based on frequency

Here's an example:

counts = l // Flatten // Counts;
mask = Map[counts[#] != 1 &, l, {2}];
Pick[l, mask]

{{"a", "b", "c"}, {"a", "b"}, {"a", "b"}, {"a", "c"}}

And for the other one,

mask = Map[counts[#] > 1 &, l, {2}];
Pick[l, And @@@ mask]

{{"a", "b", "c"}, {"a", "b"}}

Another way:

Map[
 If[counts[#] != 1, #, Nothing] &,
 l, {2}]

{{"a", "b", "c"}, {"a", "b"}, {"a", "b"}, {"a", "c"}}

If[And @@ (counts[#] > 1 & /@ #), #, Nothing] & /@ l

{{"a", "b", "c"}, {"a", "b"}}

Alternatives using Select rather than Pick:

l = {{"a", "b", "c"}, {"a", "b"}, {"a", "d", "b"}, {"a", "c", "e"}};
counts = Counts[Flatten@l];

1. To obtain the sublists whose elements are repeated in the list:

   Select[ContainsNone[Keys@Select[# == 1 &]@counts]@l
   (* Out: {{"a", "b", "c"}, {"a", "b"}} *)
   

2. To remove those sublists that contain non-repeated elements in the overall list:

   DeleteCases[Alternatives @@ Keys@Select[# == 1 &]@counts] /@ l
   (* Out: {{"a", "b", "c"}, {"a", "b"}, {"a", "b"}, {"a", "c"}} *)