Specifically, I think the "sltu" (set if less than, unsigned) instruction is useful for carries. When you add two unsigned integers, the result is smaller than the inputs if and only if an overflow occurred.

  ; a1:a0 * a2 --> a5:a4:a3
  ; using t0 as temp reg
  mulhu a5, a1, a2
  mulu  a4, a1, a2
  mulhu t0, a0, a2
  mulu  a3, a0, a2
  add   a4, a4, t0
  ; carry a 1 or a 0, overwriting t0
  sltu  t0, a4, t0
  add   a5, a5, t0

(edit: switched a1 and a0 for consistency)