just stumbled on this and confirming that this bug still exists in Octave 6.2.0:

>> a  = [1 2 3];

>> a .* a'
ans =

   1   2   3
   2   4   6
   3   6   9

>> b = sparse(a)
b =

Compressed Column Sparse (rows = 1, cols = 3, nnz = 3 [100%])

  (1, 1) -> 1
  (1, 2) -> 2
  (1, 3) -> 3

>> b .* b'
error: product: nonconformant arguments (op1 is 1x3, op2 is 3x1)

Just added a related bug for the diagonal matrices:
https://savannah.gnu.org/bugs/index.php?46110

I encountered something similar with automatic broadcasting and sparse vectors:

ones(3,10).*[0;2;0] # works as expected

ones(3,10).*sparse(2,1,2,3,1) # does not work

and yields the following error message:
error: product: nonconformant arguments (op1 is 3x10, op2 is 3x1)

I am on version 3.8.1

Sorry for the double post in ( https://savannah.gnu.org/bugs/?35787 ), feels free to removeone of them.

Broadcasting doesn't work at all for sparse matrices.  There appears to be no good workaround

#Doesn't work automatically for sparse matrix with full vector
octave:1> a = sprand(100000,100000,0.00001);
octave:2> b = rand(100000,1);
octave:3> res = a == b;
error: mx_el_eq: nonconformant arguments (op1 is 100000x100000, op2 is 100000x1)

#Doesn't work explicitly for sparse matrix with full vector
octave:9> res = bsxfun(@eq,a,b);
error: out of memory or dimension too large for Octave's index type

#Doesn't work automatically for sparse matrix with sparse vector
octave:9> b = sparse(b);
octave:10> res = a == b;
error: mx_el_eq: nonconformant arguments (op1 is 100000x100000, op2 is 100000x1)

#Doesn't work explicitly for sparse matrix with sparse vector
octave:10> res = bsxfun(@eq,a,b);
error: out of memory or dimension too large for Octave's index type

#Often there's a special-case work-around, but it's generally unwieldy

octave:10> b_mat = diag(b) * spones(a);
octave:11> [i,j] = find(a);
octave:12> res = sparse(i,j,nonzeros(a) == nonzeros(b_mat));