B737-800
Flight Crew Air Transport Pilot (ATP)
Workload; Confusion; Communication Breakdown
Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR; Inflight Event / Encounter Weather / Turbulence
General None Reported / Taken
Aircraft; Weather; Procedure; Company Policy
Left with planned arrival of 5.7 and no alternate listed or additional fuel added.  Forecast was no lower than six SM for time of arrival.  First Officer received oral ATIS for arrival calling 1/2 mile in fog (no digital ATIS). Sent ACARS message to Dispatch for amended Release and alternate airport. First Officer was doing work for weather; checks; and performance; formulated own plan for ZZZ1 as alternate and checked ZZZ2 as well. Through 18;000 FT got message from Dispatch; 'If you want to change to ZZZ1; it is 2000-pound burn and ZZZ1 weather.'  Sent ACARS to Dispatch; 'change from what?'   Descent for CAT III approach RVR 700 to 1400.  Formulated a plan for one approach and if missed; direct ZZZ1; which was VFR and we could see it 40 miles away.  Landed RVR about 1200. On rollout; received chime and additional information message from Dispatch.  5.4 at the gate in XXX.  Upon phone calls to Dispatch was told he had sent an amendment for ZZZ2 as alternate with burn and initials to us 50 miles west of ZZZ3.  I said we didn't get it.  He said he had sent it and had documentation to that effect. Also that not getting an ACARS MSG happens all the time to everyone. Dispatcher also said he was willing to 'take the hit on this one.' Have positive TWO-WAY communication. Maybe response required for Release change similar to diversion plan.  Or; since this thing happens all the time to everyone; if no response send message until you get one.
After updating destination weather which unexpectedly decreased to CAT III; the B737-800 crew requested an alternate but the ACARS with the release was not received until after landing at the filed destination.