After returning from New York on Thursday 08th June (American Airlines flight from JFK). Our plane landed at approx 0655hrs. American Airlines (AA) no doubt refused to pay Edinburgh's extortionate rates to transfer passengers via the Passenger Boarding Bridge so the cheaper alternative was to use ONE set of stairs. These stairs were NOT suited due to a malfunction. After being informed by the AA flight captain that these were not suitable, she then told us that another set of steps would be required. 15 minutes later another set of steps were driven upto the plane. When disembarking the aircraft, we were told to 'be careful' as the stairs were 'wobbly'. These stairs were a disgrace to passenger comfort and, in my opinion, they did not feel safe. We were then put onto buses to transfer us to the other side of the airport where Passport Control is situated. Whilst we were waiting on the last passengers to disembark the aeroplane, everyone's attention was drawn to the TWO elderly Japanese couple who clearly had difficulty walking, never mind dealing with the 'wobbly' stairs.They were assisted by a younger Japanese couple, but they, also looked uncomfortable coming down the stairs. As the couple struggled to come down the stairs i noticed that the 8 (EIGHT) Swissport/Menzies ground staff members, this did not include the baggage handlers who were doing their job of unloading the baggage, stood there looking at these unfortunate people. When an American sounding individual said to one of the ground staff that this incident was absurd. She replied 'Excuse me, its not my fault!' Fortunately, our aeroplane was the only one that landed and Passport Control was empty. (I have previously been queued onto the apron, in the rain, before at Edinburgh International Airport. We then waited 20 minutes on our bags coming onto the carousel. So from the flight parking at the ramp to getting our bags it took approximately 1 hour and 20 minutes. An apology from the Captain of our flight for the time it was taking to get the stairs sorted,a disgrace of equipment used in getting approximately 180 people of an aeroplane and an embarrassment of no help whatsoever from the ground crew. My partner and i live and work in Edinburgh and use the airport roughly 10 times per year. It is so sad that tourists, business people, friends and family come to see our beautiful city and have to witness this total lack of care and attention. Edinburgh Airport Limited's FIRST Passenger Commitment is: We will welcome you with a smile and excellent service. On this occasion and no doubt many others their FIRST commitment is FAILING. I sincerely hope that this honest review is received by Edinburgh Airport Limited and these types of incidents are rectified.