Question

his shoddy frock and mobile cigar have also brought (its,their) share of laughs.

Answer 1

Think of it this way.

"His shoddy frock and mobile cigar have also brought its share of laughs."

And

"His shoddy frock and mobile cigar have also brought their share of laughs."

Which one sounds better?

I'd say the first time, but that's just me. x