Regarding wheelchairs, it is often a case that the incorrect information is passed right from the moment that passengers are checked in.
Dispatchers rely on the information passed to them by their passenger handling agents, whether this be verbal or contained within the computerised check-in system. If the system has a passenger listed as a WCHR and not a WCHS or WCHC, then a WCHR will be advised to both the CC and onwards to the destination station.
However, that said, any dispatcher worth his or her salt will check prior to departure the exact level of assistance required and amend the request as necessary.
Pax are also their own worst enemy at times. They will refuse wheelchair assistance at check-in (embarassment, personal pride or whatever), and then upon arrival at the gate when they see that they have to climb steps, request assistance. As I'm sure nobody needs telling, this cannot be magically summoned with immediate effect. Or, as has been mentioned already, decide en-route that they can no longer walk and need assistance at the other end.
The situation is often complicated by pax who knowing they only have a short walk on departure, request no assistance, but on arrival at destination (say PMI where there is a substantial distance from gate to exit) do require legitimate assistance.
In a busy ops office, these things can be easily overlooked.
From the flight deck point of view, CC should notify the flight crew of any special requests whilst giving their pre-departure report. The PNF should ensure this is written on the PLOG and passed to the handlers upon contact. However, sometimes this is forgotten, and in the busier airports this unfortunately leads to lengthy delays.
Relying on the departure station to pass an accurate movement message is not foolproof. Some stations are excellent, some are not. Very often overseas stations, where communication between the CC and dispatcher is difficult due to limited spoken English (or any other common language), information is misunderstood or not understood at all, and therefore not passed correctly.
It is an imperfect system, with plentiful scope at all stages for human error. The best any of us can do is ensure we try to play our part, and manage the situation as best we can when the system fails.